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We propose a novel model for refugee housing respecting the preferences of accepting community and refugees themselves. In particular, we are given a topology representing the local community, a set of inhabitants occupying some vertices of the topology, and a set of refugees that should be housed on the empty vertices of graph. Both the inhabitants and the refugees have preferences over the structure of their neighbourhood. We are specifically interested in the problem of finding housings such that the preferences of every individual are met; using game-theoretical words, we are looking for housings that are stable with respect to some well-defined notion of stability. We investigate conditions under which the existence of equilibria is guaranteed and study the computational complexity of finding such a stable outcome. As the problem is NP-hard even in very simple settings, we employ the parameterised complexity framework to give a finer-grained view on the problem's complexity with respect to natural parameters and structural restrictions of the given topology.

Host Community Respecting Refugee Housing

2023-02-27 20:42:03

Dušan Knop, Šimon Schierreich

http://arxiv.org/abs/2302.13997v2, http://arxiv.org/pdf/2302.13997v2

cs.GT

th

There is increasing regulatory interest in whether machine learning algorithms deployed in consequential domains (e.g. in criminal justice) treat different demographic groups "fairly." However, there are several proposed notions of fairness, typically mutually incompatible. Using criminal justice as an example, we study a model in which society chooses an incarceration rule. Agents of different demographic groups differ in their outside options (e.g. opportunity for legal employment) and decide whether to commit crimes. We show that equalizing type I and type II errors across groups is consistent with the goal of minimizing the overall crime rate; other popular notions of fairness are not.

Fair Prediction with Endogenous Behavior

2020-02-18 19:07:25

Christopher Jung, Sampath Kannan, Changhwa Lee, Mallesh M. Pai, Aaron Roth, Rakesh Vohra

http://arxiv.org/abs/2002.07147v1, http://arxiv.org/pdf/2002.07147v1

econ.TH

th

In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP's beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader's optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson's optimal auction theory. We generalize Myerson's virtual values, and characterize the profit-maximizing IC AMM. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way.

A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers

2023-03-01 06:21:29

Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden

http://dx.doi.org/10.4230/LIPIcs.ITCS.2024.80, http://arxiv.org/abs/2303.00208v2, http://arxiv.org/pdf/2303.00208v2

cs.GT

th

This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximiser principal. Building upon the so-called dynamic programming approach in Cvitani\'c, Possama\"i, and Touzi [18] and the recently available results in Hern\'andez and Possama\"i [43], we present a methodology that covers the previous contracting problem. Our main contribution consists in a characterisation of the moral hazard problem faced by the principal. In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts. Nevertheless, this characterisation yields, as far as we know, a novel class of control problems that involve the control of a forward Volterra equation via Volterra-type controls, and infinite-dimensional stochastic target constraints. Despite the inherent challenges associated to such a problem, we study the solution under three different specifications of utility functions for both the agent and the principal, and draw qualitative implications from the form of the optimal contract. The general case remains the subject of future research.

Time-inconsistent contract theory

2023-03-03 00:52:39

Camilo Hernández, Dylan Possamaï

http://arxiv.org/abs/2303.01601v1, http://arxiv.org/pdf/2303.01601v1

econ.TH

th

Information design in an incomplete information game includes a designer with the goal of influencing players' actions through signals generated from a designed probability distribution so that its objective function is optimized. We consider a setting in which the designer has partial knowledge on agents' utilities. We address the uncertainty about players' preferences by formulating a robust information design problem against worst case payoffs. If the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, then the information design problem under quadratic design objectives is a semidefinite program (SDP). Specifically, we consider ellipsoid perturbations over payoff coefficients in linear-quadratic-Gaussian (LQG) games. We show that this leads to a tractable robust SDP formulation. Numerical studies are carried out to identify the relation between the perturbation levels and the optimal information structures.

Robust Social Welfare Maximization via Information Design in Linear-Quadratic-Gaussian Games

2023-03-09 21:40:39

Furkan Sezer, Ceyhun Eksin

http://arxiv.org/abs/2303.05489v2, http://arxiv.org/pdf/2303.05489v2

math.OC

th

Consider a normal location model $X \mid \theta \sim N(\theta, \sigma^2)$ with known $\sigma^2$. Suppose $\theta \sim G_0$, where the prior $G_0$ has zero mean and unit variance. Let $G_1$ be a possibly misspecified prior with zero mean and unit variance. We show that the squared error Bayes risk of the posterior mean under $G_1$ is bounded, uniformly over $G_0, G_1, \sigma^2 > 0$.

Mean-variance constrained priors have finite maximum Bayes risk in the normal location model

2023-03-15 17:36:08

Jiafeng Chen

http://arxiv.org/abs/2303.08653v1, http://arxiv.org/pdf/2303.08653v1

math.ST

th

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

The Moderating Effect of Instant Runoff Voting

2023-03-17 05:37:27

Kiran Tomlinson, Johan Ugander, Jon Kleinberg

http://arxiv.org/abs/2303.09734v5, http://arxiv.org/pdf/2303.09734v5

cs.MA

th

We study the complexity of finding an approximate (pure) Bayesian Nash equilibrium in a first-price auction with common priors when the tie-breaking rule is part of the input. We show that the problem is PPAD-complete even when the tie-breaking rule is trilateral (i.e., it specifies item allocations when no more than three bidders are in tie, and adopts the uniform tie-breaking rule otherwise). This is the first hardness result for equilibrium computation in first-price auctions with common priors. On the positive side, we give a PTAS for the problem under the uniform tie-breaking rule.

Complexity of Equilibria in First-Price Auctions under General Tie-Breaking Rules

2023-03-29 04:57:34

Xi Chen, Binghui Peng

http://arxiv.org/abs/2303.16388v1, http://arxiv.org/pdf/2303.16388v1

cs.GT

th

Since Kopel's duopoly model was proposed about three decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap. This paper analyzes the asymmetric duopoly model of Kopel analytically by using several tools based on symbolic computations. We discuss the possibility of the existence of multiple positive equilibria and establish necessary and sufficient conditions for a given number of positive equilibria to exist. The possible positions of the equilibria in Kopel's model are also explored. Furthermore, in the asymmetric model of Kopel, if the duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the local stability of equilibria for the first time. The occurrence of chaos in Kopel's model seems to be supported by observations through numerical simulations, which, however, is challenging to prove rigorously. The second objective is to prove the existence of snapback repellers in Kopel's map, which implies the existence of chaos in the sense of Li-Yorke according to Marotto's theorem.

Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

2023-04-05 00:35:38

Xiaoliang Li, Kongyan Chen, Wei Niu, Bo Huang

http://arxiv.org/abs/2304.02136v2, http://arxiv.org/pdf/2304.02136v2

math.DS

th

This article investigates mechanism-based explanations for a well-known empirical pattern in sociology of education, namely, that Black-White unequal access to school resources -- defined as advanced coursework -- is the highest in racially diverse and majority-White schools. Through an empirically calibrated and validated agent-based model, this study explores the dynamics of two qualitatively informed mechanisms, showing (1) that we have reason to believe that the presence of White students in school can influence the emergence of Black-White advanced enrollment disparities and (2) that such influence can represent another possible explanation for the macro-level pattern of interest. Results contribute to current scholarly accounts of within-school inequalities, shedding light into policy strategies to improve the educational experiences of Black students in racially integrated settings.

The presence of White students and the emergence of Black-White within-school inequalities: two interaction-based mechanisms

2023-04-10 23:09:47

João M. Souto-Maior

http://arxiv.org/abs/2304.04849v4, http://arxiv.org/pdf/2304.04849v4

physics.soc-ph

th

The study of systemic risk is often presented through the analysis of several measures referring to quantities used by practitioners and policy makers. Almost invariably, those measures evaluate the size of the impact that exogenous events can exhibit on a financial system without analysing the nature of initial shock. Here we present a symmetric approach and propose a set of measures that are based on the amount of exogenous shock that can be absorbed by the system before it starts to deteriorate. For this purpose, we use a linearized version of DebtRank that allows to clearly show the onset of financial distress towards a correct systemic risk estimation. We show how we can explicitly compute localized and uniform exogenous shocks and explained their behavior though spectral graph theory. We also extend analysis to heterogeneous shocks that have to be computed by means of Monte Carlo simulations. We believe that our approach is more general and natural and allows to express in a standard way the failure risk in financial systems.

Systemic risk measured by systems resiliency to initial shocks

2023-04-12 15:13:46

Luka Klinčić, Vinko Zlatić, Guido Caldarelli, Hrvoje Štefančić

http://arxiv.org/abs/2304.05794v1, http://arxiv.org/pdf/2304.05794v1

physics.soc-ph

th

Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are widely studied in game theory, economics, and multiagent systems. Equilibrium concepts are invariant under certain transforms of the payoffs. We define an equilibrium-inspired distance metric for the space of all normal-form games and uncover a distance-preserving equilibrium-invariant embedding. Furthermore, we propose an additional transform which defines a better-response-invariant distance metric and embedding. To demonstrate these metric spaces we study $2\times2$ games. The equilibrium-invariant embedding of $2\times2$ games has an efficient two variable parameterization (a reduction from eight), where each variable geometrically describes an angle on a unit circle. Interesting properties can be spatially inferred from the embedding, including: equilibrium support, cycles, competition, coordination, distances, best-responses, and symmetries. The best-response-invariant embedding of $2\times2$ games, after considering symmetries, rediscovers a set of 15 games, and their respective equivalence classes. We propose that this set of game classes is fundamental and captures all possible interesting strategic interactions in $2\times2$ games. We introduce a directed graph representation and name for each class. Finally, we leverage the tools developed for $2\times2$ games to develop game theoretic visualizations of large normal-form and extensive-form games that aim to fingerprint the strategic interactions that occur within.

Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of $2\times2$ Normal-Form Games

2023-04-20 00:31:28

Luke Marris, Ian Gemp, Georgios Piliouras

http://arxiv.org/abs/2304.09978v1, http://arxiv.org/pdf/2304.09978v1

cs.GT

th

In dynamic environments, Q-learning is an automaton that (i) provides estimates (Q-values) of the continuation values associated with each available action; and (ii) follows the naive policy of almost always choosing the action with highest Q-value. We consider a family of automata that are based on Q-values but whose policy may systematically favor some actions over others, for example through a bias that favors cooperation. In the spirit of Compte and Postlewaite [2018], we look for equilibrium biases within this family of Q-based automata. We examine classic games under various monitoring technologies and find that equilibrium biases may strongly foster collusion.

Q-learning with biased policy rules

2023-04-25 11:25:10

Olivier Compte

http://arxiv.org/abs/2304.12647v2, http://arxiv.org/pdf/2304.12647v2

econ.TH

th

The logistics of urban areas are becoming more sophisticated due to the fast city population growth. The stakeholders are faced with the challenges of the dynamic complexity of city logistics(CL) systems characterized by the uncertainty effect together with the freight vehicle emissions causing pollution. In this conceptual paper, we present a research methodology for the environmental sustainability of CL systems that can be attained by effective stakeholders' collaboration under non-chaotic situations and the presumption of the human levity tendency. We propose the mathematical axioms of the uncertainty effect while putting forward the notion of condition effectors, and how to assign hypothetical values to them. Finally, we employ a spider network and causal loop diagram to investigate the system's elements and their behavior over time.

Modeling the Complexity of City Logistics Systems for Sustainability

2023-04-27 10:21:56

Taiwo Adetiloye, Anjali Awasthi

http://arxiv.org/abs/2304.13987v1, http://arxiv.org/pdf/2304.13987v1

math.OC

th

This paper provides a systematic study of the robust Stackelberg equilibrium (RSE), which naturally generalizes the widely adopted solution concept of the strong Stackelberg equilibrium (SSE). The RSE accounts for any possible up-to-$\delta$ suboptimal follower responses in Stackelberg games and is adopted to improve the robustness of the leader's strategy. While a few variants of robust Stackelberg equilibrium have been considered in previous literature, the RSE solution concept we consider is importantly different -- in some sense, it relaxes previously studied robust Stackelberg strategies and is applicable to much broader sources of uncertainties. We provide a thorough investigation of several fundamental properties of RSE, including its utility guarantees, algorithmics, and learnability. We first show that the RSE we defined always exists and thus is well-defined. Then we characterize how the leader's utility in RSE changes with the robustness level considered. On the algorithmic side, we show that, in sharp contrast to the tractability of computing an SSE, it is NP-hard to obtain a fully polynomial approximation scheme (FPTAS) for any constant robustness level. Nevertheless, we develop a quasi-polynomial approximation scheme (QPTAS) for RSE. Finally, we examine the learnability of the RSE in a natural learning scenario, where both players' utilities are not known in advance, and provide almost tight sample complexity results on learning the RSE. As a corollary of this result, we also obtain an algorithm for learning SSE, which strictly improves a key result of Bai et al. in terms of both utility guarantee and computational efficiency.

Robust Stackelberg Equilibria

2023-04-28 20:19:21

Jiarui Gan, Minbiao Han, Jibang Wu, Haifeng Xu

http://arxiv.org/abs/2304.14990v2, http://arxiv.org/pdf/2304.14990v2

cs.GT

th

In the past several decades, the world's economy has become increasingly globalized. On the other hand, there are also ideas advocating the practice of ``buy local'', by which people buy locally produced goods and services rather than those produced farther away. In this paper, we establish a mathematical theory of real price that determines the optimal global versus local spending of an agent which achieves the agent's optimal tradeoff between spending and obtained utility. Our theory of real price depends on the asymptotic analysis of a Markov chain transition probability matrix related to the network of producers and consumers. We show that the real price of a product or service can be determined from the involved Markov chain matrix, and can be dramatically different from the product's label price. In particular, we show that the label prices of products and services are often not ``real'' or directly ``useful'': given two products offering the same myopic utility, the one with lower label price may not necessarily offer better asymptotic utility. This theory shows that the globality or locality of the products and services does have different impacts on the spending-utility tradeoff of a customer. The established mathematical theory of real price can be used to determine whether to adopt or not to adopt certain artificial intelligence (AI) technologies from an economic perspective.

To AI or not to AI, to Buy Local or not to Buy Local: A Mathematical Theory of Real Price

2023-05-09 05:43:47

Huan Cai, Catherine Xu, Weiyu Xu

http://arxiv.org/abs/2305.05134v1, http://arxiv.org/pdf/2305.05134v1

econ.TH

th

A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize welfare functions that reward more balanced surplus allocations. Our main result is the surprising existence of a novel signaling scheme that simultaneously $8$-approximates all welfare functions that are non-negative, monotonically increasing, symmetric, and concave, compared with any other signaling scheme. Classical examples of such welfare functions include the utilitarian social welfare, the Nash welfare, and the max-min welfare. Such a guarantee cannot be given by any consumer-surplus-maximizing scheme -- which are the ones typically studied in the literature. In addition, our scheme is socially efficient, and has the fairness property that buyers with higher values enjoy higher expected surplus, which is not always the case for existing schemes.

Fair Price Discrimination

2023-05-11 20:45:06

Siddhartha Banerjee, Kamesh Munagala, Yiheng Shen, Kangning Wang

http://arxiv.org/abs/2305.07006v1, http://arxiv.org/pdf/2305.07006v1

cs.GT

th

We show that computing the optimal social surplus requires $\Omega(mn)$ bits of communication between the website and the bidders in a sponsored search auction with $n$ slots on the website and with tick size of $2^{-m}$ in the discrete model, even when bidders are allowed to freely communicate with each other.

Social Surplus Maximization in Sponsored Search Auctions Requires Communication

2023-05-12 21:49:03

Suat Evren

http://arxiv.org/abs/2305.07729v1, http://arxiv.org/pdf/2305.07729v1

cs.GT

th

A seller wants to sell an item to n buyers. Buyer valuations are drawn i.i.d. from a distribution unknown to the seller; the seller only knows that the support is included in [a, b]. To be robust, the seller chooses a DSIC mechanism that optimizes the worst-case performance relative to the first-best benchmark. Our analysis unifies the regret and the ratio objectives. For these objectives, we derive an optimal mechanism and the corresponding performance in quasi-closed form, as a function of the support information and the number of buyers n. Our analysis reveals three regimes of support information and a new class of robust mechanisms. i.) With "low" support information, the optimal mechanism is a second-price auction (SPA) with random reserve, a focal class in earlier literature. ii.) With "high" support information, SPAs are strictly suboptimal, and an optimal mechanism belongs to a class of mechanisms we introduce, which we call pooling auctions (POOL); whenever the highest value is above a threshold, the mechanism still allocates to the highest bidder, but otherwise the mechanism allocates to a uniformly random buyer, i.e., pools low types. iii.) With "moderate" support information, a randomization between SPA and POOL is optimal. We also characterize optimal mechanisms within nested central subclasses of mechanisms: standard mechanisms that only allocate to the highest bidder, SPA with random reserve, and SPA with no reserve. We show strict separations in terms of performance across classes, implying that deviating from standard mechanisms is necessary for robustness.

Robust Auction Design with Support Information

2023-05-16 02:23:22

Jerry Anunrojwong, Santiago R. Balseiro, Omar Besbes

http://arxiv.org/abs/2305.09065v2, http://arxiv.org/pdf/2305.09065v2

econ.TH

th

In this paper, we navigate the intricate domain of reviewer rewards in open-access academic publishing, leveraging the precision of mathematics and the strategic acumen of game theory. We conceptualize the prevailing voucher-based reviewer reward system as a two-player game, subsequently identifying potential shortcomings that may incline reviewers towards binary decisions. To address this issue, we propose and mathematically formalize an alternative reward system with the objective of mitigating this bias and promoting more comprehensive reviews. We engage in a detailed investigation of the properties and outcomes of both systems, employing rigorous game-theoretical analysis and deep reinforcement learning simulations. Our results underscore a noteworthy divergence between the two systems, with our proposed system demonstrating a more balanced decision distribution and enhanced stability. This research not only augments the mathematical understanding of reviewer reward systems, but it also provides valuable insights for the formulation of policies within journal review system. Our contribution to the mathematical community lies in providing a game-theoretical perspective to a real-world problem and in the application of deep reinforcement learning to simulate and understand this complex system.

Game-Theoretical Analysis of Reviewer Rewards in Peer-Review Journal Systems: Analysis and Experimental Evaluation using Deep Reinforcement Learning

2023-05-20 07:13:35

Minhyeok Lee

http://arxiv.org/abs/2305.12088v1, http://arxiv.org/pdf/2305.12088v1

cs.AI

th

This paper evaluates market equilibrium under different pricing mechanisms in a two-settlement 100%-renewables electricity market. Given general probability distributions of renewable energy, we establish game-theoretical models to analyze equilibrium bidding strategies, market prices, and profits under uniform pricing (UP) and pay-as-bid pricing (PAB). We prove that UP can incentivize suppliers to withhold bidding quantities and lead to price spikes. PAB can reduce the market price, but it may lead to a mixed-strategy price equilibrium. Then, we present a regulated uniform pricing scheme (RUP) based on suppliers' marginal costs that include penalty costs for real-time deviations. We show that RUP can achieve lower yet positive prices and profits compared with PAB in a duopoly market, which approximates the least-cost system outcome. Simulations with synthetic and real data find that under PAB and RUP, higher uncertainty of renewables and real-time shortage penalty prices can increase the market price by encouraging lower bidding quantities, thereby increasing suppliers' profits.

Uniform Pricing vs Pay as Bid in 100%-Renewables Electricity Markets: A Game-theoretical Analysis

2023-05-21 03:50:39

Dongwei Zhao, Audun Botterud, Marija Ilic

http://arxiv.org/abs/2305.12309v1, http://arxiv.org/pdf/2305.12309v1

eess.SY

th

During epidemics people reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision making depends on knowledge about vaccination timing in a differential game in which individual decision making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We show that the earlier the vaccination is expected to happen and the more precisely the timing of the vaccination is known, the stronger is the incentive to socially distance. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Rational social distancing in epidemics with uncertain vaccination timing

2023-05-23 05:28:14

Simon K. Schnyder, John J. Molina, Ryoichi Yamamoto, Matthew S. Turner

http://arxiv.org/abs/2305.13618v1, http://arxiv.org/pdf/2305.13618v1

econ.TH

th

Sociologists of education increasingly highlight the role of opportunity hoarding in the formation of Black-White educational inequalities. Informed by this literature, this article unpacks the necessary and sufficient conditions under which the hoarding of educational resources emerges within schools. It develops a qualitatively informed agent-based model which captures Black and White students' competition for a valuable school resource: advanced coursework. In contrast to traditional accounts -- which explain the emergence of hoarding through the actions of Whites that keep valuable resources within White communities -- simulations, perhaps surprisingly, show hoarding to arise even when Whites do not play the role of hoarders of resources. Behind this result is the fact that a structural inequality (i.e., racial differences in social class) -- and not action-driven hoarding -- is the necessary condition for hoarding to emerge. Findings, therefore, illustrate that common action-driven understandings of opportunity hoarding can overlook the structural foundations behind this important phenomenon. Policy implications are discussed.

Hoarding without hoarders: unpacking the emergence of opportunity hoarding within schools

2023-05-24 05:49:38

João M. Souto-Maior

http://arxiv.org/abs/2305.14653v2, http://arxiv.org/pdf/2305.14653v2

physics.soc-ph

th

We design TimeBoost: a practical transaction ordering policy for rollup sequencers that takes into account both transaction timestamps and bids; it works by creating a score from timestamps and bids, and orders transactions based on this score. TimeBoost is transaction-data-independent (i.e., can work with encrypted transactions) and supports low transaction finalization times similar to a first-come first-serve (FCFS or pure-latency) ordering policy. At the same time, it avoids the inefficient latency competition created by an FCFS policy. It further satisfies useful economic properties of first-price auctions that come with a pure-bidding policy. We show through rigorous economic analyses how TimeBoost allows players to compete on arbitrage opportunities in a way that results in better guarantees compared to both pure-latency and pure-bidding approaches.

Buying Time: Latency Racing vs. Bidding in Transaction Ordering

2023-06-03 22:20:39

Akaki Mamageishvili, Mahimna Kelkar, Jan Christoph Schlegel, Edward W. Felten

http://arxiv.org/abs/2306.02179v2, http://arxiv.org/pdf/2306.02179v2

cs.GT

th

Models of social learning feature either binary signals or abstract signal structures often deprived of micro-foundations. Both models are limited when analyzing interim results or performing empirical analysis. We present a method of generating signal structures which are richer than the binary model, yet are tractable enough to perform simulations and empirical analysis. We demonstrate the method's usability by revisiting two classical papers: (1) we discuss the economic significance of unbounded signals Smith and Sorensen (2000); (2) we use experimental data from Anderson and Holt (1997) to perform econometric analysis. Additionally, we provide a necessary and sufficient condition for the occurrence of action cascades.

A Practical Approach to Social Learning

2020-02-25 19:41:23

Amir Ban, Moran Koren

http://arxiv.org/abs/2002.11017v1, http://arxiv.org/pdf/2002.11017v1

econ.TH

th

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

Coordinated Dynamic Bidding in Repeated Second-Price Auctions with Budgets

2023-06-13 14:55:04

Yurong Chen, Qian Wang, Zhijian Duan, Haoran Sun, Zhaohua Chen, Xiang Yan, Xiaotie Deng

http://arxiv.org/abs/2306.07709v1, http://arxiv.org/pdf/2306.07709v1

cs.GT

th

We study the classic house-swapping problem of Shapley and Scarf (1974) in a setting where agents may have "objective" indifferences, i.e., indifferences that are shared by all agents. In other words, if any one agent is indifferent between two houses, then all agents are indifferent between those two houses. The most direct interpretation is the presence of multiple copies of the same object. Our setting is a special case of the house-swapping problem with general indifferences. We derive a simple, easily interpretable algorithm that produces the unique strict core allocation of the house-swapping market, if it exists. Our algorithm runs in square polynomial time, a substantial improvement over the cubed time methods for the more general problem.

House-Swapping with Objective Indifferences

2023-06-16 01:16:22

Will Sandholtz, Andrew Tai

http://arxiv.org/abs/2306.09529v1, http://arxiv.org/pdf/2306.09529v1

econ.TH

th

This paper extends the Isotonic Mechanism from the single-owner to multi-owner settings, in an effort to make it applicable to peer review where a paper often has multiple authors. Our approach starts by partitioning all submissions of a machine learning conference into disjoint blocks, each of which shares a common set of co-authors. We then employ the Isotonic Mechanism to elicit a ranking of the submissions from each author and to produce adjusted review scores that align with both the reported ranking and the original review scores. The generalized mechanism uses a weighted average of the adjusted scores on each block. We show that, under certain conditions, truth-telling by all authors is a Nash equilibrium for any valid partition of the overlapping ownership sets. However, we demonstrate that while the mechanism's performance in terms of estimation accuracy depends on the partition structure, optimizing this structure is computationally intractable in general. We develop a nearly linear-time greedy algorithm that provably finds a performant partition with appealing robust approximation guarantees. Extensive experiments on both synthetic data and real-world conference review data demonstrate the effectiveness of this generalized Isotonic Mechanism.

An Isotonic Mechanism for Overlapping Ownership

2023-06-19 23:33:25

Jibang Wu, Haifeng Xu, Yifan Guo, Weijie Su

http://arxiv.org/abs/2306.11154v1, http://arxiv.org/pdf/2306.11154v1

cs.GT

th

We study the power of menus of contracts in principal-agent problems with adverse selection (agents can be one of several types) and moral hazard (we cannot observe agent actions directly). For principal-agent problems with $T$ types and $n$ actions, we show that the best menu of contracts can obtain a factor $\Omega(\max(n, \log T))$ more utility for the principal than the best individual contract, partially resolving an open question of Guruganesh et al. (2021). We then turn our attention to randomized menus of linear contracts, where we likewise show that randomized linear menus can be $\Omega(T)$ better than the best single linear contract. As a corollary, we show this implies an analogous gap between deterministic menus of (general) contracts and randomized menus of contracts (as introduced by Castiglioni et al. (2022)).

The Power of Menus in Contract Design

2023-06-22 07:28:44

Guru Guruganesh, Jon Schneider, Joshua Wang, Junyao Zhao

http://arxiv.org/abs/2306.12667v1, http://arxiv.org/pdf/2306.12667v1

cs.GT

th

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). As such, we embed the black-box procedure of solving an integer linear program into a framework that is explainable from start to finish. Moreover, we study the axiomatic properties of the proposed methods by embedding our framework into the rich literature of cooperative bargaining and probabilistic social choice. Lastly, we evaluate the proposed methods on a specific application, namely kidney exchange. We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

Fair integer programming under dichotomous preferences

2023-06-23 12:06:13

Tom Demeulemeester, Dries Goossens, Ben Hermans, Roel Leus

http://arxiv.org/abs/2306.13383v1, http://arxiv.org/pdf/2306.13383v1

cs.GT

th

In this paper we give the first explicit enumeration of all maximal Condorcet domains on $n\leq 7$ alternatives. This has been accomplished by developing a new algorithm for constructing Condorcet domains, and an implementation of that algorithm which has been run on a supercomputer. We follow this up by the first survey of the properties of all maximal Condorcet domains up to degree 7, with respect to many properties studied in the social sciences and mathematical literature. We resolve several open questions posed by other authors, both by examples from our data and theorems. We give a new set of results on the symmetry properties of Condorcet domains which unify earlier works. Finally we discuss connections to other domain types such as non-dictatorial domains and generalisations of single-peaked domains. All our data is made freely available for other researches via a new website.

Condorcet Domains of Degree at most Seven

2023-06-28 11:05:06

Dolica Akello-Egwell, Charles Leedham-Green, Alastair Litterick, Klas Markström, Søren Riis

http://arxiv.org/abs/2306.15993v5, http://arxiv.org/pdf/2306.15993v5

cs.DM

th

The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's fundamental idea is to eliminate risk by hedging the option by purchasing and selling the underlying asset in a specific way, that is, to replicate the payoff of the option with a portfolio (which continuously trades the underlying) whose value at each time can be verified. One of the most crucial, yet restrictive, assumptions for this task is that the market follows a geometric Brownian motion, which has been relaxed and generalized in various ways. The concept of robust finance revolves around developing models that account for uncertainties and variations in financial markets. Martingale Optimal Transport, which is an adaptation of the Optimal Transport theory to the robust financial framework, is one of the most prominent directions. In this paper, we consider market models with arbitrarily many underlying assets whose values are observed over arbitrarily many time periods, and demonstrates the existence of a portfolio sub- or super-hedging a general path-dependent derivative security in terms of trading European options and underlyings, as well as the portfolio replicating the derivative payoff when the market model yields the extremal price of the derivative given marginal distributions of the underlyings. In mathematical terms, this paper resolves the question of dual attainment for the multi-period vectorial martingale optimal transport problem.

Replication of financial derivatives under extreme market models given marginals

2023-07-03 10:44:59

Tongseok Lim

http://arxiv.org/abs/2307.00807v1, http://arxiv.org/pdf/2307.00807v1

q-fin.MF

th

Classification algorithms are increasingly used in areas such as housing, credit, and law enforcement in order to make decisions affecting peoples' lives. These algorithms can change individual behavior deliberately (a fraud prediction algorithm deterring fraud) or inadvertently (content sorting algorithms spreading misinformation), and they are increasingly facing public scrutiny and regulation. Some of these regulations, like the elimination of cash bail in some states, have focused on \textit{lowering the stakes of certain classifications}. In this paper we characterize how optimal classification by an algorithm designer can affect the distribution of behavior in a population -- sometimes in surprising ways. We then look at the effect of democratizing the rewards and punishments, or stakes, to algorithmic classification to consider how a society can potentially stem (or facilitate!) predatory classification. Our results speak to questions of algorithmic fairness in settings where behavior and algorithms are interdependent, and where typical measures of fairness focusing on statistical accuracy across groups may not be appropriate.

Algorithms, Incentives, and Democracy

2023-07-05 17:22:01

Elizabeth Maggie Penn, John W. Patty

http://arxiv.org/abs/2307.02319v1, http://arxiv.org/pdf/2307.02319v1

econ.TH

th

We study Proportional Response Dynamics (PRD) in linear Fisher markets where participants act asynchronously. We model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. We show that if every bidder individually uses the PRD update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. Our proof technique uncovers further properties of linear Fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.

Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling

2023-07-09 09:31:20

Yoav Kolumbus, Menahem Levy, Noam Nisan

http://arxiv.org/abs/2307.04108v1, http://arxiv.org/pdf/2307.04108v1

cs.GT

th

In an information aggregation game, a set of senders interact with a receiver through a mediator. Each sender observes the state of the world and communicates a message to the mediator, who recommends an action to the receiver based on the messages received. The payoff of the senders and of the receiver depend on both the state of the world and the action selected by the receiver. This setting extends the celebrated cheap talk model in two aspects: there are many senders (as opposed to just one) and there is a mediator. From a practical perspective, this setting captures platforms in which strategic experts advice is aggregated in service of action recommendations to the user. We aim at finding an optimal mediator/platform that maximizes the users' welfare given highly resilient incentive compatibility requirements on the equilibrium selected: we want the platform to be incentive compatible for the receiver/user when selecting the recommended action, and we want it to be resilient against group deviations by the senders/experts. We provide highly positive answers to this challenge, manifested through efficient algorithms.

Resilient Information Aggregation

2023-07-11 10:06:13

Itai Arieli, Ivan Geffner, Moshe Tennenholtz

http://dx.doi.org/10.4204/EPTCS.379.6, http://arxiv.org/abs/2307.05054v1, http://arxiv.org/pdf/2307.05054v1

econ.TH

th

With a novel search algorithm or assortment planning or assortment optimization algorithm that takes into account a Bayesian approach to information updating and two-stage assortment optimization techniques, the current research provides a novel concept of competitiveness in the digital marketplace. Via the search algorithm, there is competition between the platform, vendors, and private brands of the platform. The current paper suggests a model and discusses how competition and collusion arise in the digital marketplace through assortment planning or assortment optimization algorithm. Furthermore, it suggests a model of an assortment algorithm free from collusion between the platform and the large vendors. The paper's major conclusions are that collusive assortment may raise a product's purchase likelihood but fail to maximize expected revenue. The proposed assortment planning, on the other hand, maintains competitiveness while maximizing expected revenue.

A Model of Competitive Assortment Planning Algorithm

2023-07-16 17:15:18

Dipankar Das

http://arxiv.org/abs/2307.09479v1, http://arxiv.org/pdf/2307.09479v1

econ.TH

th

We consider manipulations in the context of coalitional games, where a coalition aims to increase the total payoff of its members. An allocation rule is immune to coalitional manipulation if no coalition can benefit from internal reallocation of worth on the level of its subcoalitions (reallocation-proofness), and if no coalition benefits from a lower worth while all else remains the same (weak coalitional monotonicity). Replacing additivity in Shapley's original characterization by these requirements yields a new foundation of the Shapley value, i.e., it is the unique efficient and symmetric allocation rule that awards nothing to a null player and is immune to coalitional manipulations. We further find that for efficient allocation rules, reallocation-proofness is equivalent to constrained marginality, a weaker variant of Young's marginality axiom. Our second characterization improves upon Young's characterization by weakening the independence requirement intrinsic to marginality.

Coalitional Manipulations and Immunity of the Shapley Value

2023-10-31 15:43:31

Christian Basteck, Frank Huettner

http://arxiv.org/abs/2310.20415v1, http://arxiv.org/pdf/2310.20415v1

econ.TH

th

A growing number of central authorities use assignment mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms give students an incentive to be strategic and misreport their preferences. In this paper, we provide an identification approach for causal effects of school assignment on future outcomes that accounts for strategic misreporting. Misreporting may invalidate existing point-identification approaches, and we derive sharp bounds for causal effects that are robust to strategic behavior. Our approach applies to any mechanism as long as there exist placement scores and cutoffs that characterize that mechanism's allocation rule. We use data from a deferred acceptance mechanism that assigns students to more than 1,000 university-major combinations in Chile. Students behave strategically because the mechanism in Chile constrains the number of majors that students submit in their preferences to eight options. Our methodology takes that into account and partially identifies the effect of changes in school assignment on various graduation outcomes.

Causal Effects in Matching Mechanisms with Strategically Reported Preferences

2023-07-26 19:35:42

Marinho Bertanha, Margaux Luflade, Ismael Mourifié

http://arxiv.org/abs/2307.14282v1, http://arxiv.org/pdf/2307.14282v1

econ.EM

th

We present a new optimization-based method for aggregating preferences in settings where each decision maker, or voter, expresses preferences over pairs of alternatives. The challenge is to come up with a ranking that agrees as much as possible with the votes cast in cases when some of the votes conflict. Only a collection of votes that contains no cycles is non-conflicting and can induce a partial order over alternatives. Our approach is motivated by the observation that a collection of votes that form a cycle can be treated as ties. The method is then to remove unions of cycles of votes, or circulations, from the vote graph and determine aggregate preferences from the remainder. We introduce the strong maximum circulation which is formed by a union of cycles, the removal of which guarantees a unique outcome in terms of the induced partial order. Furthermore, it contains all the aggregate preferences remaining following the elimination of any maximum circulation. In contrast, the well-known, optimization-based, Kemeny method has non-unique output and can return multiple, conflicting rankings for the same input. In addition, Kemeny's method requires solving an NP-hard problem, whereas our algorithm is efficient, based on network flow techniques, and runs in strongly polynomial time, independent of the number of votes. We address the construction of a ranking from the partial order and show that rankings based on a convex relaxation of Kemeny's model are consistent with our partial order. We then study the properties of removing a maximal circulation versus a maximum circulation and establish that, while maximal circulations will in general identify a larger number of aggregate preferences, the partial orders induced by the removal of different maximal circulations are not unique and may be conflicting. Moreover, finding a minimum maximal circulation is an NP-hard problem.

The Strong Maximum Circulation Algorithm: A New Method for Aggregating Preference Rankings

2023-07-28 20:51:05

Nathan Atkinson, Scott C. Ganz, Dorit S. Hochbaum, James B. Orlin

http://arxiv.org/abs/2307.15702v1, http://arxiv.org/pdf/2307.15702v1

cs.SI

th

We study the impact of data sharing policies on cyber insurance markets. These policies have been proposed to address the scarcity of data about cyber threats, which is essential to manage cyber risks. We propose a Cournot duopoly competition model in which two insurers choose the number of policies they offer (i.e., their production level) and also the resources they invest to ensure the quality of data regarding the cost of claims (i.e., the data quality of their production cost). We find that enacting mandatory data sharing sometimes creates situations in which at most one of the two insurers invests in data quality, whereas both insurers would invest when information sharing is not mandatory. This raises concerns about the merits of making data sharing mandatory.

Duopoly insurers' incentives for data quality under a mandatory cyber data sharing regime

2023-05-29 23:19:14

Carlos Barreto, Olof Reinert, Tobias Wiesinger, Ulrik Franke

http://dx.doi.org/10.1016/j.cose.2023.103292, http://arxiv.org/abs/2308.00795v1, http://arxiv.org/pdf/2308.00795v1

econ.TH

th

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players--constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the $\beta$-measure, and construct an axiomatisation of the Gately measure.

Game theoretic foundations of the Gately power measure for directed networks

2023-08-04 15:00:28

Robert P. Gilles, Lina Mallozzi

http://arxiv.org/abs/2308.02274v1, http://arxiv.org/pdf/2308.02274v1

cs.GT

th

Major advances in Machine Learning (ML) and Artificial Intelligence (AI) increasingly take the form of developing and releasing general-purpose models. These models are designed to be adapted by other businesses and agencies to perform a particular, domain-specific function. This process has become known as adaptation or fine-tuning. This paper offers a model of the fine-tuning process where a Generalist brings the technological product (here an ML model) to a certain level of performance, and one or more Domain-specialist(s) adapts it for use in a particular domain. Both entities are profit-seeking and incur costs when they invest in the technology, and they must reach a bargaining agreement on how to share the revenue for the technology to reach the market. For a relatively general class of cost and revenue functions, we characterize the conditions under which the fine-tuning game yields a profit-sharing solution. We observe that any potential domain-specialization will either contribute, free-ride, or abstain in their uptake of the technology, and we provide conditions yielding these different strategies. We show how methods based on bargaining solutions and sub-game perfect equilibria provide insights into the strategic behavior of firms in these types of interactions, and we find that profit-sharing can still arise even when one firm has significantly higher costs than another. We also provide methods for identifying Pareto-optimal bargaining arrangements for a general set of utility functions.

Fine-Tuning Games: Bargaining and Adaptation for General-Purpose Models

2023-08-08 20:01:42

Benjamin Laufer, Jon Kleinberg, Hoda Heidari

http://arxiv.org/abs/2308.04399v2, http://arxiv.org/pdf/2308.04399v2

cs.GT

th

Fairness is one of the most desirable societal principles in collective decision-making. It has been extensively studied in the past decades for its axiomatic properties and has received substantial attention from the multiagent systems community in recent years for its theoretical and computational aspects in algorithmic decision-making. However, these studies are often not sufficiently rich to capture the intricacies of human perception of fairness in the ambivalent nature of the real-world problems. We argue that not only fair solutions should be deemed desirable by social planners (designers), but they should be governed by human and societal cognition, consider perceived outcomes based on human judgement, and be verifiable. We discuss how achieving this goal requires a broad transdisciplinary approach ranging from computing and AI to behavioral economics and human-AI interaction. In doing so, we identify shortcomings and long-term challenges of the current literature of fair division, describe recent efforts in addressing them, and more importantly, highlight a series of open research directions.

The Fairness Fair: Bringing Human Perception into Collective Decision-Making

2023-12-22 06:06:24

Hadi Hosseini

http://arxiv.org/abs/2312.14402v1, http://arxiv.org/pdf/2312.14402v1

cs.AI

th

In the committee selection problem, the goal is to choose a subset of size $k$ from a set of candidates $C$ that collectively gives the best representation to a set of voters. We consider this problem in Euclidean $d$-space where each voter/candidate is a point and voters' preferences are implicitly represented by Euclidean distances to candidates. We explore fault-tolerance in committee selection and study the following three variants: (1) given a committee and a set of $f$ failing candidates, find their optimal replacement; (2) compute the worst-case replacement score for a given committee under failure of $f$ candidates; and (3) design a committee with the best replacement score under worst-case failures. The score of a committee is determined using the well-known (min-max) Chamberlin-Courant rule: minimize the maximum distance between any voter and its closest candidate in the committee. Our main results include the following: (1) in one dimension, all three problems can be solved in polynomial time; (2) in dimension $d \geq 2$, all three problems are NP-hard; and (3) all three problems admit a constant-factor approximation in any fixed dimension, and the optimal committee problem has an FPT bicriterion approximation.

Fault Tolerance in Euclidean Committee Selection

2023-08-14 19:50:48

Chinmay Sonar, Subhash Suri, Jie Xue

http://arxiv.org/abs/2308.07268v1, http://arxiv.org/pdf/2308.07268v1

cs.GT

th

Monetary conditions are frequently cited as a significant factor influencing fluctuations in commodity prices. However, the precise channels of transmission are less well identified. In this paper, we develop a unified theory to study the impact of interest rates on commodity prices and the underlying mechanisms. To that end, we extend the competitive storage model to accommodate stochastically evolving interest rates, and establish general conditions under which (i) a unique rational expectations equilibrium exists and can be efficiently computed, and (ii) interest rates are negatively correlated with commodity prices. As an application, we quantify the impact of interest rates on commodity prices through the speculative channel, namely, the role of speculators in the physical market whose incentive to hold inventories is influenced by interest rate movements. Our findings demonstrate that real interest rates have nontrivial and persistent negative effect on commodity prices, and the magnitude of the impact varies substantially under different market supply and interest rate regimes.

Interest Rate Dynamics and Commodity Prices

2023-08-15 08:10:35

Christophe Gouel, Qingyin Ma, John Stachurski

http://arxiv.org/abs/2308.07577v1, http://arxiv.org/pdf/2308.07577v1

econ.TH

th

Classic optimal transport theory is built on minimizing the expected cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost. This new formulation is motivated by concrete problems in decision theory, robust optimization, and risk management, and it has many distinct features compared to the classic theory. We choose simple cost functions and study different distortion functions and their implications on the optimal transport plan. We show that on the real line, the comonotonic coupling is optimal for the distorted optimal transport problem when the distortion function is convex and the cost function is submodular and monotone. Some forms of duality and uniqueness results are provided. For inverse-S-shaped distortion functions and linear cost, we obtain the unique form of optimal coupling for all marginal distributions, which turns out to have an interesting ``first comonotonic, then counter-monotonic" dependence structure; for S-shaped distortion functions a similar structure is obtained. Our results highlight several challenges and features in distorted optimal transport, offering a new mathematical bridge between the fields of probability, decision theory, and risk management.

Distorted optimal transport

2023-08-22 10:25:51

Haiyan Liu, Bin Wang, Ruodu Wang, Sheng Chao Zhuang

http://arxiv.org/abs/2308.11238v1, http://arxiv.org/pdf/2308.11238v1

math.OC

th

In 1979, Weitzman introduced Pandora's box problem as a framework for sequential search with costly inspections. Recently, there has been a surge of interest in Pandora's box problem, particularly among researchers working at the intersection of economics and computation. This survey provides an overview of the recent literature on Pandora's box problem, including its latest extensions and applications in areas such as market design, decision theory, and machine learning.

Recent Developments in Pandora's Box Problem: Variants and Applications

2023-08-23 19:39:14

Hedyeh Beyhaghi, Linda Cai

http://arxiv.org/abs/2308.12242v1, http://arxiv.org/pdf/2308.12242v1

cs.GT

th

We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that almost every game that is 'generic' (without indifferences) and has a pure Nash equilibrium and a 'large' number of players is connected, meaning that every action profile that is not a pure Nash equilibrium can reach every pure Nash equilibrium via best-response paths. This has important implications for dynamics in games. In particular, we show that there are simple, uncoupled, adaptive dynamics for which period-by-period play converges almost surely to a pure Nash equilibrium in almost every large generic game that has one (which contrasts with the known fact that there is no such dynamic that leads almost surely to a pure Nash equilibrium in every generic game that has one). We build on recent results in probabilistic combinatorics for our characterisation of game connectivity.

Game Connectivity and Adaptive Dynamics

2023-09-19 16:32:34

Tom Johnston, Michael Savery, Alex Scott, Bassel Tarbush

http://arxiv.org/abs/2309.10609v3, http://arxiv.org/pdf/2309.10609v3

econ.TH

th

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons to be uncertain about updating, rationality can require you to prefer ignorance.

Rational Aversion to Information

2023-09-21 06:51:52

Sven Neth

http://dx.doi.org/10.1086/727772, http://arxiv.org/abs/2309.12374v3, http://arxiv.org/pdf/2309.12374v3

stat.OT

th

Community rating is a policy that mandates uniform premium regardless of the risk factors. In this paper, our focus narrows to the single contract interpretation wherein we establish a theoretical framework for community rating using Stiglitz's (1977) monopoly model in which there is a continuum of agents. We exhibit profitability conditions and show that, under mild regularity conditions, the optimal premium is unique and satisfies the inverse elasticity rule. Our numerical analysis, using realistic parameter values, reveals that under regulation, a 10% increase in indemnity is possible with minimal impact on other variables.

Theoretical Foundations of Community Rating by a Private Monopolist Insurer: Framework, Regulation, and Numerical Analysis

2023-09-27 00:02:00

Yann Braouezec, John Cagnol

http://arxiv.org/abs/2309.15269v2, http://arxiv.org/pdf/2309.15269v2

econ.TH

th

This paper fundamentally reformulates economic and financial theory to include electronic currencies. The valuation of the electronic currencies will be based on macroeconomic theory and the fundamental equation of monetary policy, not the microeconomic theory of discounted cash flows. The view of electronic currency as a transactional equity associated with tangible assets of a sub-economy will be developed, in contrast to the view of stock as an equity associated mostly with intangible assets of a sub-economy. The view will be developed of the electronic currency management firm as an entity responsible for coordinated monetary (electronic currency supply and value stabilization) and fiscal (investment and operational) policies of a substantial (for liquidity of the electronic currency) sub-economy. The risk model used in the valuations and the decision-making will not be the ubiquitous, yet inappropriate, exponential risk model that leads to discount rates, but will be multi time scale models that capture the true risk. The decision-making will be approached from the perspective of true systems control based on a system response function given by the multi scale risk model and system controllers that utilize the Deep Reinforcement Learning, Generative Pretrained Transformers, and other methods of Artificial Intelligence (DRL/GPT/AI). Finally, the sub-economy will be viewed as a nonlinear complex physical system with both stable equilibriums that are associated with short-term exploitation, and unstable equilibriums that need to be stabilized with active nonlinear control based on the multi scale system response functions and DRL/GPT/AI.

A new economic and financial theory of money

2023-10-08 06:16:06

Michael E. Glinsky, Sharon Sievert

http://arxiv.org/abs/2310.04986v4, http://arxiv.org/pdf/2310.04986v4

econ.TH

th

We propose an operating-envelope-aware, prosumer-centric, and efficient energy community that aggregates individual and shared community distributed energy resources and transacts with a regulated distribution system operator (DSO) under a generalized net energy metering tariff design. To ensure safe network operation, the DSO imposes dynamic export and import limits, known as dynamic operating envelopes, on end-users' revenue meters. Given the operating envelopes, we propose an incentive-aligned community pricing mechanism under which the decentralized optimization of community members' benefit implies the optimization of overall community welfare. The proposed pricing mechanism satisfies the cost-causation principle and ensures the stability of the energy community in a coalition game setting. Numerical examples provide insights into the characteristics of the proposed pricing mechanism and quantitative measures of its performance.

Operating-Envelopes-Aware Decentralized Welfare Maximization for Energy Communities

2023-10-11 06:04:34

Ahmed S. Alahmed, Guido Cavraro, Andrey Bernstein, Lang Tong

http://arxiv.org/abs/2310.07157v1, http://arxiv.org/pdf/2310.07157v1

eess.SY

th

Sustainability of common-pool resources hinges on the interplay between human and environmental systems. However, there is still a lack of a novel and comprehensive framework for modelling extraction of common-pool resources and cooperation of human agents that can account for different factors that shape the system behavior and outcomes. In particular, we still lack a critical value for ensuring resource sustainability under different scenarios. In this paper, we present a novel framework for studying resource extraction and cooperation in human-environmental systems for common-pool resources. We explore how different factors, such as resource availability and conformity effect, influence the players' decisions and the resource outcomes. We identify critical values for ensuring resource sustainability under various scenarios. We demonstrate the observed phenomena are robust to the complexity and assumptions of the models and discuss implications of our study for policy and practice, as well as the limitations and directions for future research.

Impact of resource availability and conformity effect on sustainability of common-pool resources

2023-10-11 18:18:13

Chengyi Tu, Renfei Chen, Ying Fan, Xuwei Pan

http://arxiv.org/abs/2310.07577v2, http://arxiv.org/pdf/2310.07577v2

econ.TH

th

Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a contact, are all examples of (dynamic) stochastic differential games. In essence, game theory deals with the analysis of strategic interactions among multiple decision-makers. The theory has had enormous impact in a wide variety of fields, but its rigorous mathematical analysis is rather recent. It started with the pioneering work of von Neumann and Morgenstern published in 1944. Since then, game theory has taken centre stage in applied mathematics and related areas. Game theory has also played an important role in unsuspected areas: for instance in military applications, when the analysis of guided interceptor missiles in the 1950s motivated the study of games evolving dynamically in time. Such games (when possibly subject to randomness) are called stochastic differential games. Their study started with the work of Issacs, who crucially recognised the importance of (stochastic) control theory in the area. Over the past few decades since Isaacs's work, a rich theory of stochastic differential game has emerged and branched into several directions. This paper will review recent advances in the study of solvability of stochastic differential games, with a focus on a purely probabilistic technique to approach the problem. Unsurprisingly, the number of players involved in the game is a major factor of the analysis. We will explain how the size of the population impacts the analyses and solvability of the problem, and discuss mean field games as well as the convergence of finite player games to mean field games.

On the population size in stochastic differential games

2023-10-15 22:06:56

Dylan Possamaï, Ludovic Tangpi

http://arxiv.org/abs/2310.09919v1, http://arxiv.org/pdf/2310.09919v1

math.PR

th

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we prove that a game satisfies the minimax property along with all its subgames if and only if none of its subgames is isomorphic to the "larger number game." This generalizes a recent theorem of Hanneke, Livni and Moran. We also propose several applications of our results outside of game theory.

The minimax property in infinite two-person win-lose games

2023-10-30 10:21:52

Ron Holzman

http://arxiv.org/abs/2310.19314v1, http://arxiv.org/pdf/2310.19314v1

cs.GT

th

A cake allocation is called *strongly-proportional* if it allocates each agent a piece worth for them strictly more than their fair share of 1/n the total cake value. It is called *connected* if it allocates each agent a connected piece. We present a necessary and sufficient condition for the existence of a strongly-proportional connected cake-allocation among agents with strictly positive valuations.

On Connected Strongly-Proportional Cake-Cutting

2023-12-23 22:08:46

Zsuzsanna Jankó, Attila Joó, Erel Segal-Halevi

http://arxiv.org/abs/2312.15326v1, http://arxiv.org/pdf/2312.15326v1

math.CO

th

In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related notions have been the main explanations so far. We explain this rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering the best option, the offer is rejected. This principle qualifies as a rational punishing behavior and it replaces the experimentally falsified classical rationality (the subgame perfect Nash equilibrium) that leads to accepting any non-zero offer. The principle is implemented via the transitive regret theory for probabilistic lotteries. The expected utility implementation is a limiting case of this. We show that several experimental results normally prescribed to fairness and intent-recognition can be given an alternative explanation via rational punishment; e.g. the comparison between "fair" and "superfair", the behavior under raising the stakes etc. Hence we also propose experiments that can distinguish these two scenarios (fairness versus regret-based punishment). They assume different utilities for the proposer and responder. We focus on the mini-ultimatum version of the game and also show how it can emerge from a more general setup of the game.

Ultimatum game: regret or fairness?

2023-11-07 11:54:02

Lida H. Aleksanyan, Armen E. Allahverdyan, Vardan G. Bardakhchyan

http://arxiv.org/abs/2311.03814v1, http://arxiv.org/pdf/2311.03814v1

econ.TH

th

We introduce and mathematically study a conceptual model for the dynamics of the buyers population in markets of perishable goods where prices are not posted. Buyers behaviours are driven partly by loyalty to previously visited merchants and partly by sensitivity to merchants intrinsic attractiveness. Moreover, attractiveness evolve in time depending on the relative volumes of buyers, assuming profit/competitiveness optimisation when favourable/unfavourable. While this negative feedback mechanism is a source of instability that promotes oscillatory behaviour, our analysis identifies those critical features that are responsible for the asymptotic stability of stationary states, both in their immediate neighbourhood and globally in phase space. In particular, we show that while full loss of clientele occurs (depending on the initial state) in case of a bounded reactivity rate, it cannot happen when this rate is unbounded and merchants resilience always prevails in this case. Altogether, our analysis provides mathematical insights into the consequences of introducing feedback into buyer-seller interactions and their diversified impacts on the long term levels of clientele in the markets.

Population dynamics in fresh product markets with no posted prices

2023-11-07 16:38:17

Ali Ellouze, Bastien Fernandez

http://arxiv.org/abs/2311.03987v1, http://arxiv.org/pdf/2311.03987v1

econ.TH

th

Formally, for common knowledge to arise in a dynamic setting, knowledge that it has arisen must be simultaneously attained by all players. As a result, new common knowledge is unattainable in many realistic settings, due to timing frictions. This unintuitive phenomenon, observed by Halpern and Moses (1990), was discussed by Arrow et al. (1987) and by Aumann (1989), was called a paradox by Morris (2014), and has evaded satisfactory resolution for four decades. We resolve this paradox by proposing a new definition for common knowledge, which coincides with the traditional one in static settings but generalizes it in dynamic settings. Under our definition, common knowledge can arise without simultaneity, particularly in canonical examples of the Haplern-Moses paradox. We demonstrate its usefulness by deriving for it an agreement theorem \`a la Aumann (1976), and showing that it arises in the setting of Geanakoplos and Polemarchakis (1982) with timing frictions added.

Common Knowledge, Regained

2023-11-08 01:38:16

Yannai A. Gonczarowski, Yoram Moses

http://arxiv.org/abs/2311.04374v1, http://arxiv.org/pdf/2311.04374v1

econ.TH

th

We investigate the problem of approximating an incomplete preference relation $\succsim$ on a finite set by a complete preference relation. We aim to obtain this approximation in such a way that the choices on the basis of two preferences, one incomplete, the other complete, have the smallest possible discrepancy in the aggregate. To this end, we use the top-difference metric on preferences, and define a best complete approximation of $\succsim$ as a complete preference relation nearest to $\succsim$ relative to this metric. We prove that such an approximation must be a maximal completion of $\succsim$, and that it is, in fact, any one completion of $\succsim$ with the largest index. Finally, we use these results to provide a sufficient condition for the best complete approximation of a preference to be its canonical completion. This leads to closed-form solutions to the best approximation problem in the case of several incomplete preference relations of interest.

Best Complete Approximations of Preference Relations

2023-11-11 21:45:59

Hiroki Nishimura, Efe A. Ok

http://arxiv.org/abs/2311.06641v1, http://arxiv.org/pdf/2311.06641v1

econ.TH

th

We study a repeated Principal Agent problem between a long lived Principal and Agent pair in a prior free setting. In our setting, the sequence of realized states of nature may be adversarially chosen, the Agent is non-myopic, and the Principal aims for a strong form of policy regret. Following Camara, Hartline, and Johnson, we model the Agent's long-run behavior with behavioral assumptions that relax the common prior assumption (for example, that the Agent has no swap regret). Within this framework, we revisit the mechanism proposed by Camara et al., which informally uses calibrated forecasts of the unknown states of nature in place of a common prior. We give two main improvements. First, we give a mechanism that has an exponentially improved dependence (in terms of both running time and regret bounds) on the number of distinct states of nature. To do this, we show that our mechanism does not require truly calibrated forecasts, but rather forecasts that are unbiased subject to only a polynomially sized collection of events -- which can be produced with polynomial overhead. Second, in several important special cases -- including the focal linear contracting setting -- we show how to remove strong ``Alignment'' assumptions (which informally require that near-ties are always broken in favor of the Principal) by specifically deploying ``stable'' policies that do not have any near ties that are payoff relevant to the Principal. Taken together, our new mechanism makes the compelling framework proposed by Camara et al. much more powerful, now able to be realized over polynomially sized state spaces, and while requiring only mild assumptions on Agent behavior.

Efficient Prior-Free Mechanisms for No-Regret Agents

2023-11-14 00:13:42

Natalie Collina, Aaron Roth, Han Shao

http://arxiv.org/abs/2311.07754v1, http://arxiv.org/pdf/2311.07754v1

cs.GT

th

How can an informed sender persuade a receiver, having only limited information about the receiver's beliefs? Motivated by research showing generative AI can simulate economic agents, we initiate the study of information design with an oracle. We assume the sender can learn more about the receiver by querying this oracle, e.g., by simulating the receiver's behavior. Aside from AI motivations such as general-purpose Large Language Models (LLMs) and problem-specific machine learning models, alternate motivations include customer surveys and querying a small pool of live users. Specifically, we study Bayesian Persuasion where the sender has a second-order prior over the receiver's beliefs. After a fixed number of queries to an oracle to refine this prior, the sender commits to an information structure. Upon receiving the message, the receiver takes a payoff-relevant action maximizing her expected utility given her posterior beliefs. We design polynomial-time querying algorithms that optimize the sender's expected utility in this Bayesian Persuasion game. As a technical contribution, we show that queries form partitions of the space of receiver beliefs that can be used to quantify the sender's knowledge.

Algorithmic Persuasion Through Simulation: Information Design in the Age of Generative AI

2023-11-30 02:01:33

Keegan Harris, Nicole Immorlica, Brendan Lucier, Aleksandrs Slivkins

http://arxiv.org/abs/2311.18138v1, http://arxiv.org/pdf/2311.18138v1

cs.GT

th

We analyze the overall benefits of an energy community cooperative game under which distributed energy resources (DER) are shared behind a regulated distribution utility meter under a general net energy metering (NEM) tariff. Two community DER scheduling algorithms are examined. The first is a community with centrally controlled DER, whereas the second is decentralized letting its members schedule their own DER locally. For both communities, we prove that the cooperative game's value function is superadditive, hence the grand coalition achieves the highest welfare. We also prove the balancedness of the cooperative game under the two DER scheduling algorithms, which means that there is a welfare re-distribution scheme that de-incentivizes players from leaving the grand coalition to form smaller ones. Lastly, we present five ex-post and an ex-ante welfare re-distribution mechanisms and evaluate them in simulation, in addition to investigating the performance of various community sizes under the two DER scheduling algorithms.

Resource Sharing in Energy Communities: A Cooperative Game Approach

2023-11-30 21:41:16

Ahmed S. Alahmed, Lang Tong

http://arxiv.org/abs/2311.18792v1, http://arxiv.org/pdf/2311.18792v1

cs.GT

th

The field of algorithmic fairness has rapidly emerged over the past 15 years as algorithms have become ubiquitous in everyday lives. Algorithmic fairness traditionally considers statistical notions of fairness algorithms might satisfy in decisions based on noisy data. We first show that these are theoretically disconnected from welfare-based notions of fairness. We then discuss two individual welfare-based notions of fairness, envy freeness and prejudice freeness, and establish conditions under which they are equivalent to error rate balance and predictive parity, respectively. We discuss the implications of these findings in light of the recently discovered impossibility theorem in algorithmic fairness (Kleinberg, Mullainathan, & Raghavan (2016), Chouldechova (2017)).

Algorithmic Fairness with Feedback

2023-12-06 00:42:14

John W. Patty, Elizabeth Maggie Penn

http://arxiv.org/abs/2312.03155v1, http://arxiv.org/pdf/2312.03155v1

econ.TH

th

Multiwinner voting captures a wide variety of settings, from parliamentary elections in democratic systems to product placement in online shopping platforms. There is a large body of work dealing with axiomatic characterizations, computational complexity, and algorithmic analysis of multiwinner voting rules. Although many challenges remain, significant progress has been made in showing existence of fair and representative outcomes as well as efficient algorithmic solutions for many commonly studied settings. However, much of this work focuses on single-shot elections, even though in numerous real-world settings elections are held periodically and repeatedly. Hence, it is imperative to extend the study of multiwinner voting to temporal settings. Recently, there have been several efforts to address this challenge. However, these works are difficult to compare, as they model multi-period voting in very different ways. We propose a unified framework for studying temporal fairness in this domain, drawing connections with various existing bodies of work, and consolidating them within a general framework. We also identify gaps in existing literature, outline multiple opportunities for future work, and put forward a vision for the future of multiwinner voting in temporal settings.

Temporal Fairness in Multiwinner Voting

2023-12-07 19:38:32

Edith Elkind, Svetlana Obraztsova, Nicholas Teh

http://arxiv.org/abs/2312.04417v2, http://arxiv.org/pdf/2312.04417v2

cs.GT

th

Reducing wealth inequality and disparity is a global challenge. The economic system is mainly divided into (1) gift and reciprocity, (2) power and redistribution, (3) market exchange, and (4) mutual aid without reciprocal obligations. The current inequality stems from a capitalist economy consisting of (2) and (3). To sublimate (1), which is the human economy, to (4), the concept of a "mixbiotic society" has been proposed in the philosophical realm. This is a society in which free and diverse individuals, "I," mix with each other, recognize their respective "fundamental incapability" and sublimate them into "WE" solidarity. The economy in this society must have moral responsibility as a coadventurer and consideration for vulnerability to risk. Therefore, I focus on two factors of mind perception: moral responsibility and risk vulnerability, and propose a novel model of wealth distribution following an econophysical approach. Specifically, I developed a joint-venture model, a redistribution model in the joint-venture model, and a "WE economy" model. A simulation comparison of a combination of the joint ventures and redistribution with the WE economies reveals that WE economies are effective in reducing inequality and resilient in normalizing wealth distribution as advantages, and susceptible to free riders as disadvantages. However, this disadvantage can be compensated for by fostering consensus and fellowship, and by complementing it with joint ventures. This study essentially presents the effectiveness of moral responsibility, the complementarity between the WE economy and the joint economy, and the direction of the economy toward reducing inequality. Future challenges are to develop the WE economy model based on real economic analysis and psychology, as well as to promote WE economy fieldwork for worker coops and platform cooperatives to realize a desirable mixbiotic society.

WE economy: Potential of mutual aid distribution based on moral responsibility and risk vulnerability

2023-12-12 04:52:45

Takeshi Kato

http://arxiv.org/abs/2312.06927v1, http://arxiv.org/pdf/2312.06927v1

econ.TH

th

The Council of the European Union (EU) is one of the main decision-making bodies of the EU. Many decisions require a qualified majority: the support of 55% of the member states (currently 15) that represent at least 65% of the total population. We investigate how the power distribution, based on the Shapley-Shubik index, and the proportion of winning coalitions change if these criteria are modified within reasonable bounds. The influence of the two countries with about 4% of the total population each is found to be almost flat. The level of decisiveness decreases if the population criterion is above 68% or the states criterion is at least 17. The proportion of winning coalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximal relative change in the Shapley--Shubik indices remains below 3.5% (5.5%). Our results are indispensable to evaluate any proposal for reforming the qualified majority voting system.

Voting power in the Council of the European Union: A comprehensive sensitivity analysis

2023-12-28 11:07:33

Dóra Gréta Petróczy, László Csató

http://arxiv.org/abs/2312.16878v1, http://arxiv.org/pdf/2312.16878v1

physics.soc-ph

th

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-\`a-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.

The Relative Value of Prediction in Algorithmic Decision Making

2023-12-13 23:52:45

Juan Carlos Perdomo

http://arxiv.org/abs/2312.08511v1, http://arxiv.org/pdf/2312.08511v1

cs.CY

th

A linear-quadratic-Gaussian (LQG) game is an incomplete information game with quadratic payoff functions and Gaussian payoff states. This study addresses an information design problem to identify an information structure that maximizes a quadratic objective function. Gaussian information structures are found to be optimal among all information structures. Furthermore, the optimal Gaussian information structure can be determined by semidefinite programming, which is a natural extension of linear programming. This paper provides sufficient conditions for the optimality and suboptimality of both no and full information disclosure. In addition, we characterize optimal information structures in symmetric LQG games and optimal public information structures in asymmetric LQG games, with each structure presented in a closed-form expression.

LQG Information Design

2023-12-15 04:36:36

Masaki Miyashita, Takashi Ui

http://arxiv.org/abs/2312.09479v1, http://arxiv.org/pdf/2312.09479v1

econ.TH

th

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents.

Better Foundations for Subjective Probability

2023-12-15 16:52:17

Sven Neth

http://arxiv.org/abs/2312.09796v1, http://arxiv.org/pdf/2312.09796v1

stat.OT

th

Algorithmic monoculture arises when many decision-makers rely on the same algorithm to evaluate applicants. An emerging body of work investigates possible harms of this kind of homogeneity, but has been limited by the challenge of incorporating market effects in which the preferences and behavior of many applicants and decision-makers jointly interact to determine outcomes. Addressing this challenge, we introduce a tractable theoretical model of algorithmic monoculture in a two-sided matching market with many participants. We use the model to analyze outcomes under monoculture (when decision-makers all evaluate applicants using a common algorithm) and under polyculture (when decision-makers evaluate applicants independently). All else equal, monoculture (1) selects less-preferred applicants when noise is well-behaved, (2) matches more applicants to their top choice, though individual applicants may be worse off depending on their value to decision-makers and risk tolerance, and (3) is more robust to disparities in the number of applications submitted.

Monoculture in Matching Markets

2023-12-15 17:46:54

Kenny Peng, Nikhil Garg

http://arxiv.org/abs/2312.09841v1, http://arxiv.org/pdf/2312.09841v1

cs.GT

th

While there is universal agreement that agents ought to act ethically, there is no agreement as to what constitutes ethical behaviour. To address this problem, recent philosophical approaches to `moral uncertainty' propose aggregation of multiple ethical theories to guide agent behaviour. However, one of the foundational proposals for aggregation - Maximising Expected Choiceworthiness (MEC) - has been criticised as being vulnerable to fanaticism; the problem of an ethical theory dominating agent behaviour despite low credence (confidence) in said theory. Fanaticism thus undermines the `democratic' motivation for accommodating multiple ethical perspectives. The problem of fanaticism has not yet been mathematically defined. Representing moral uncertainty as an instance of social welfare aggregation, this paper contributes to the field of moral uncertainty by 1) formalising the problem of fanaticism as a property of social welfare functionals and 2) providing non-fanatical alternatives to MEC, i.e. Highest k-trimmed Mean and Highest Median.

Moral Uncertainty and the Problem of Fanaticism

2023-12-18 19:09:09

Jazon Szabo, Jose Such, Natalia Criado, Sanjay Modgil

http://arxiv.org/abs/2312.11589v1, http://arxiv.org/pdf/2312.11589v1

cs.AI

th

Control barrier functions (CBFs) and safety-critical control have seen a rapid increase in popularity in recent years, predominantly applied to systems in aerospace, robotics and neural network controllers. Control barrier functions can provide a computationally efficient method to monitor arbitrary primary controllers and enforce state constraints to ensure overall system safety. One area that has yet to take advantage of the benefits offered by CBFs is the field of finance and economics. This manuscript re-introduces three applications of traditional control to economics, and develops and implements CBFs for such problems. We consider the problem of optimal advertising for the deterministic and stochastic case and Merton's portfolio optimization problem. Numerical simulations are used to demonstrate the effectiveness of using traditional control solutions in tandem with CBFs and stochastic CBFs to solve such problems in the presence of state constraints.

Stochastic Control Barrier Functions for Economics

2023-12-20 00:34:54

David van Wijk

http://arxiv.org/abs/2312.12612v1, http://arxiv.org/pdf/2312.12612v1

econ.TH

th

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways.

An extension of May's Theorem to three alternatives: axiomatizing Minimax voting

2023-12-21 22:18:28

Wesley H. Holliday, Eric Pacuit

http://arxiv.org/abs/2312.14256v1, http://arxiv.org/pdf/2312.14256v1

econ.TH

th

The ongoing rapid development of the e-commercial and interest-base websites make it more pressing to evaluate objects' accurate quality before recommendation by employing an effective reputation system. The objects' quality are often calculated based on their historical information, such as selected records or rating scores, to help visitors to make decisions before watching, reading or buying. Usually high quality products obtain a higher average ratings than low quality products regardless of rating biases or errors. However many empirical cases demonstrate that consumers may be misled by rating scores added by unreliable users or deliberate tampering. In this case, users' reputation, i.e., the ability to rating trustily and precisely, make a big difference during the evaluating process. Thus, one of the main challenges in designing reputation systems is eliminating the effects of users' rating bias on the evaluation results. To give an objective evaluation of each user's reputation and uncover an object's intrinsic quality, we propose an iterative balance (IB) method to correct users' rating biases. Experiments on two online video-provided Web sites, namely MovieLens and Netflix datasets, show that the IB method is a highly self-consistent and robust algorithm and it can accurately quantify movies' actual quality and users' stability of rating. Compared with existing methods, the IB method has higher ability to find the "dark horses", i.e., not so popular yet good movies, in the Academy Awards.

Eliminating the effect of rating bias on reputation systems

2018-01-17 19:24:03

Leilei Wu, Zhuoming Ren, Xiao-Long Ren, Jianlin Zhang, Linyuan Lü

http://arxiv.org/abs/1801.05734v1, http://arxiv.org/pdf/1801.05734v1

physics.soc-ph

th

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy that is initially rare. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. We present an algorithm for the case where mutations are restricted to pure strategies, and present experiments on several game classes including random and a recently-proposed cancer model. Our algorithm is based on a mixed-integer non-convex feasibility program formulation, which constitutes the first general optimization formulation for this problem. It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach. However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size.

Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations

2018-03-01 23:08:21

Sam Ganzfried

http://arxiv.org/abs/1803.00607v2, http://arxiv.org/pdf/1803.00607v2

cs.GT

th

In an economic market, sellers, infomediaries and customers constitute an economic network. Each seller has her own customer group and the seller's private customers are unobservable to other sellers. Therefore, a seller can only sell commodities among her own customers unless other sellers or infomediaries share her sale information to their customer groups. However, a seller is not incentivized to share others' sale information by default, which leads to inefficient resource allocation and limited revenue for the sale. To tackle this problem, we develop a novel mechanism called customer sharing mechanism (CSM) which incentivizes all sellers to share each other's sale information to their private customer groups. Furthermore, CSM also incentivizes all customers to truthfully participate in the sale. In the end, CSM not only allocates the commodities efficiently but also optimizes the seller's revenue.

Customer Sharing in Economic Networks with Costs

2018-07-18 11:55:27

Bin Li, Dong Hao, Dengji Zhao, Tao Zhou

http://arxiv.org/abs/1807.06822v1, http://arxiv.org/pdf/1807.06822v1

cs.GT

th

We consider a network of agents. Associated with each agent are her covariate and outcome. Agents influence each other's outcomes according to a certain connection/influence structure. A subset of the agents participate on a platform, and hence, are observable to it. The rest are not observable to the platform and are called the latent agents. The platform does not know the influence structure of the observable or the latent parts of the network. It only observes the data on past covariates and decisions of the observable agents. Observable agents influence each other both directly and indirectly through the influence they exert on the latent agents. We investigate how the platform can estimate the dependence of the observable agents' outcomes on their covariates, taking the latent agents into account. First, we show that this relationship can be succinctly captured by a matrix and provide an algorithm for estimating it under a suitable approximate sparsity condition using historical data of covariates and outcomes for the observable agents. We also obtain convergence rates for the proposed estimator despite the high dimensionality that allows more agents than observations. Second, we show that the approximate sparsity condition holds under the standard conditions used in the literature. Hence, our results apply to a large class of networks. Finally, we apply our results to two practical settings: targeted advertising and promotional pricing. We show that by using the available historical data with our estimator, it is possible to obtain asymptotically optimal advertising/pricing decisions, despite the presence of latent agents.

Latent Agents in Networks: Estimation and Targeting

2018-08-14 22:57:55

Baris Ata, Alexandre Belloni, Ozan Candogan

http://arxiv.org/abs/1808.04878v3, http://arxiv.org/pdf/1808.04878v3

cs.SI

th

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.

Multilinear Superhedging of Lookback Options

2018-10-05 01:50:42

Alex Garivaltis

http://arxiv.org/abs/1810.02447v2, http://arxiv.org/pdf/1810.02447v2

q-fin.PR

th

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The system problem exhibits a two-layer structure comprised of a permutation profile and optimal allocations given the permutation profile. For any fixed permutation profile, we provide a market-based mechanism to find the optimal allocations and prove the existence of equilibrium prices. We show that the system problem has a duality gap, in general, and that the primal problem is NP-hard. We then consider a relaxation of the system problem and derive some qualitative features of the optimal lottery structure.

Optimal Resource Allocation over Networks via Lottery-Based Mechanisms

2018-12-03 04:04:36

Soham R. Phade, Venkat Anantharam

http://dx.doi.org/10.1007/978-3-030-16989-3_4, http://arxiv.org/abs/1812.00501v1, http://arxiv.org/pdf/1812.00501v1

econ.TH

th

Spending by the UK's National Health Service (NHS) on independent healthcare treatment has been increased in recent years and is predicted to sustain its upward trend with the forecast of population growth. Some have viewed this increase as an attempt not to expand the patients' choices but to privatize public healthcare. This debate poses a social dilemma whether the NHS should stop cooperating with Private providers. This paper contributes to healthcare economic modelling by investigating the evolution of cooperation among three proposed populations: Public Healthcare Providers, Private Healthcare Providers and Patients. The Patient population is included as a main player in the decision-making process by expanding patient's choices of treatment. We develop a generic basic model that measures the cost of healthcare provision based on given parameters, such as NHS and private healthcare providers' cost of investments in both sectors, cost of treatments and gained benefits. A patient's costly punishment is introduced as a mechanism to enhance cooperation among the three populations. Our findings show that cooperation can be improved with the introduction of punishment (patient's punishment) against defecting providers. Although punishment increases cooperation, it is very costly considering the small improvement in cooperation in comparison to the basic model.

Pathways to Good Healthcare Services and Patient Satisfaction: An Evolutionary Game Theoretical Approach

2019-07-06 18:38:33

Zainab Alalawi, The Anh Han, Yifeng Zeng, Aiman Elragig

http://dx.doi.org/10.13140/RG.2.2.30657.10086, http://arxiv.org/abs/1907.07132v1, http://arxiv.org/pdf/1907.07132v1

physics.soc-ph

th

This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hindsight for the realized sequence of asset prices. A bilinear trading strategy is a mini two-period active strategy whose final capital growth factor is linear separately in each period's gross return vector for the asset market. I apply Cover's ingenious (1991) performance-weighted averaging technique to construct a universal bilinear portfolio that is guaranteed (uniformly for all possible market behavior) to compound its money at the same asymptotic rate as the best bilinear trading strategy in hindsight. Thus, the universal bilinear portfolio asymptotically dominates the original (1-linear) universal portfolio in the same technical sense that Cover's universal portfolios asymptotically dominate all constant-rebalanced portfolios and all buy-and-hold strategies. In fact, like so many Russian dolls, one can get carried away and use these ideas to construct an endless hierarchy of ever more dominant $H$-linear universal portfolios.

A Note on Universal Bilinear Portfolios

2019-07-23 08:55:28

Alex Garivaltis

http://arxiv.org/abs/1907.09704v2, http://arxiv.org/pdf/1907.09704v2

q-fin.MF

th

We define discounted differential privacy, as an alternative to (conventional) differential privacy, to investigate privacy of evolving datasets, containing time series over an unbounded horizon. We use privacy loss as a measure of the amount of information leaked by the reports at a certain fixed time. We observe that privacy losses are weighted equally across time in the definition of differential privacy, and therefore the magnitude of privacy-preserving additive noise must grow without bound to ensure differential privacy over an infinite horizon. Motivated by the discounted utility theory within the economics literature, we use exponential and hyperbolic discounting of privacy losses across time to relax the definition of differential privacy under continual observations. This implies that privacy losses in distant past are less important than the current ones to an individual. We use discounted differential privacy to investigate privacy of evolving datasets using additive Laplace noise and show that the magnitude of the additive noise can remain bounded under discounted differential privacy. We illustrate the quality of privacy-preserving mechanisms satisfying discounted differential privacy on smart-meter measurement time-series of real households, made publicly available by Ausgrid (an Australian electricity distribution company).

Temporally Discounted Differential Privacy for Evolving Datasets on an Infinite Horizon

2019-08-12 07:25:54

Farhad Farokhi

http://arxiv.org/abs/1908.03995v2, http://arxiv.org/pdf/1908.03995v2

cs.CR

th

Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms have been developed for solving (i.e., computing a game-theoretic solution concept such as Nash equilibrium) two-player zero-sum stochastic games, research on algorithms for non-zero-sum and multiplayer stochastic games is limited. We present a new algorithm for these settings, which constitutes the first parallel algorithm for multiplayer stochastic games. We present experimental results on a 4-player stochastic game motivated by a naval strategic planning scenario, showing that our algorithm is able to quickly compute strategies constituting Nash equilibrium up to a very small degree of approximation error.

Parallel Algorithm for Approximating Nash Equilibrium in Multiplayer Stochastic Games with Application to Naval Strategic Planning

2019-10-01 07:08:14

Sam Ganzfried, Conner Laughlin, Charles Morefield

http://arxiv.org/abs/1910.00193v4, http://arxiv.org/pdf/1910.00193v4

cs.GT

th

We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the prior fastest complete algorithm on several game classes previously studied and that its runtimes even outperform the best incomplete algorithms.

Fast Complete Algorithm for Multiplayer Nash Equilibrium

2020-02-12 02:42:14

Sam Ganzfried

http://arxiv.org/abs/2002.04734v10, http://arxiv.org/pdf/2002.04734v10

cs.GT

th

This paper presents an inverse reinforcement learning~(IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions are consistent with optimizing a cost function. In a Bayesian (partially observed) setting, the inverse learner can at best identify optimality wrt the observed strategies. Our IRL algorithm identifies optimality and then constructs set-valued estimates of the cost function.To achieve this IRL objective, we use novel ideas from Bayesian revealed preferences stemming from microeconomics. We illustrate the proposed IRL scheme using two important examples of stopping time problems, namely, sequential hypothesis testing and Bayesian search. As a real-world example, we illustrate using a YouTube dataset comprising metadata from 190000 videos how the proposed IRL method predicts user engagement in online multimedia platforms with high accuracy. Finally, for finite datasets, we propose an IRL detection algorithm and give finite sample bounds on its error probabilities.

Necessary and Sufficient Conditions for Inverse Reinforcement Learning of Bayesian Stopping Time Problems

2020-07-07 17:14:12

Kunal Pattanayak, Vikram Krishnamurthy

http://arxiv.org/abs/2007.03481v6, http://arxiv.org/pdf/2007.03481v6

cs.LG

th

We consider a model of urban spatial structure proposed by Harris and Wilson (Environment and Planning A, 1978). The model consists of fast dynamics, which represent spatial interactions between locations by the entropy-maximizing principle, and slow dynamics, which represent the evolution of the spatial distribution of local factors that facilitate such spatial interactions. One known limitation of the Harris and Wilson model is that it can have multiple locally stable equilibria, leading to a dependence of predictions on the initial state. To overcome this, we employ equilibrium refinement by stochastic stability. We build on the fact that the model is a large-population potential game and that stochastically stable states in a potential game correspond to global potential maximizers. Unlike local stability under deterministic dynamics, the stochastic stability approach allows a unique and unambiguous prediction for urban spatial configurations. We show that, in the most likely spatial configuration, the number of retail agglomerations decreases either when shopping costs for consumers decrease or when the strength of agglomerative effects increases.

Stochastic stability of agglomeration patterns in an urban retail model

2020-11-13 09:31:07

Minoru Osawa, Takashi Akamatsu, Yosuke Kogure

http://arxiv.org/abs/2011.06778v1, http://arxiv.org/pdf/2011.06778v1

econ.TH

th

In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy of no advertising. Under reasonable sufficient conditions, it is proved that the proposed coopetition strategy profile Pareto-dominates the one-shot Nash equilibrium strategy. This is a very encouraging result to tackle the much more challenging problem of designing Pareto-optimal and equilibrium strategies for the considered dynamical marketing game.

Allocating marketing resources over social networks: A long-term analysis

2020-11-17 12:39:52

Vineeth S. Varma, Samson Lasaulce, Julien Mounthanyvong, Irinel-Constantin Morarescu

http://arxiv.org/abs/2011.09268v1, http://arxiv.org/pdf/2011.09268v1

econ.TH

th

We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain $R$ of normalized dimensions of $1$ and $\rho\geq 1$, and distances are measured according to the Manhattan metric. We show that the family of 'balanced' facility configurations (in which the Voronoi cells of individual facilities are equalized with respect to a number of geometric properties) is considerably richer in this metric than for Euclidean distances. Our main result considers the 'One-Round Voronoi Game' with Manhattan distances, in which first player White and then player Black each place $n$ points in $R$; each player scores the area for which one of its facilities is closer than the facilities of the opponent. We give a tight characterization: White has a winning strategy if and only if $\rho\geq n$; for all other cases, we present a winning strategy for Black.

Competitive Location Problems: Balanced Facility Location and the One-Round Manhattan Voronoi Game

2020-11-26 16:20:21

Thomas Byrne, Sándor P. Fekete, Jörg Kalcsics, Linda Kleist

http://arxiv.org/abs/2011.13275v2, http://arxiv.org/pdf/2011.13275v2

cs.CG

th

We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its choice of when to implement that strategy across a set of discrete time slots. Cooperators evolve to fixation regularly in the model when we add time slots to lattices and small-world networks, and their portion of the population grows, albeit slowly, when organisms interact in a scale-free network. This selection for cooperators occurs across a wide variety of time slots and it does so even when a crucial condition for the evolution of cooperation on graphs is violated--namely, when the ratio of benefits to costs in the PD does not exceed the number of spatially-adjacent organisms.

Temporal assortment of cooperators in the spatial prisoner's dilemma

2020-11-29 23:27:19

Tim Johnson, Oleg Smirnov

http://arxiv.org/abs/2011.14440v1, http://arxiv.org/pdf/2011.14440v1

q-bio.PE

th

Two long-lived senders play a dynamic game of competitive persuasion. Each period, each provides information to a single short-lived receiver. When the senders also set prices, we unearth a folk theorem: if they are sufficiently patient, virtually any vector of feasible and individually rational payoffs can be sustained in a subgame perfect equilibrium. Without price-setting, there is a unique subgame perfect equilibrium. In it, patient senders provide less information--maximally patient ones none.

Dynamic Competitive Persuasion

2018-11-28 19:44:01

Mark Whitmeyer

http://arxiv.org/abs/1811.11664v6, http://arxiv.org/pdf/1811.11664v6

math.PR

th

The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability. We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard. We present exact algorithms for computing a safe equilibrium in both 2 and $n$-player games, as well as scalable approximation algorithms.

Safe Equilibrium

2022-01-12 04:45:51

Sam Ganzfried

http://arxiv.org/abs/2201.04266v10, http://arxiv.org/pdf/2201.04266v10

cs.GT

th

The design of mechanisms that encourage pro-social behaviours in populations of self-regarding agents is recognised as a major theoretical challenge within several areas of social, life and engineering sciences. When interference from external parties is considered, several heuristics have been identified as capable of engineering a desired collective behaviour at a minimal cost. However, these studies neglect the diverse nature of contexts and social structures that characterise real-world populations. Here we analyse the impact of diversity by means of scale-free interaction networks with high and low levels of clustering, and test various interference mechanisms using simulations of agents facing a cooperative dilemma. Our results show that interference on scale-free networks is not trivial and that distinct levels of clustering react differently to each interference mechanism. As such, we argue that no tailored response fits all scale-free networks and present which mechanisms are more efficient at fostering cooperation in both types of networks. Finally, we discuss the pitfalls of considering reckless interference mechanisms.

Exogenous Rewards for Promoting Cooperation in Scale-Free Networks

2019-05-13 13:57:38

Theodor Cimpeanu, The Anh Han, Francisco C. Santos

http://dx.doi.org/10.1162/isal_a_00181, http://arxiv.org/abs/1905.04964v2, http://arxiv.org/pdf/1905.04964v2

cs.GT

th

The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of their emergence and an understanding of their potential systemic consequences. This article focuses on one of these patterns: nestedness. Given a network of interacting nodes, nestedness can be described as the tendency for nodes to interact with subsets of the interaction partners of better-connected nodes. Known since more than $80$ years in biogeography, nestedness has been found in systems as diverse as ecological mutualistic organizations, world trade, inter-organizational relations, among many others. This review article focuses on three main pillars: the existing methodologies to observe nestedness in networks; the main theoretical mechanisms conceived to explain the emergence of nestedness in ecological and socio-economic networks; the implications of a nested topology of interactions for the stability and feasibility of a given interacting system. We survey results from variegated disciplines, including statistical physics, graph theory, ecology, and theoretical economics. Nestedness was found to emerge both in bipartite networks and, more recently, in unipartite ones; this review is the first comprehensive attempt to unify both streams of studies, usually disconnected from each other. We believe that the truly interdisciplinary endeavour -- while rooted in a complex systems perspective -- may inspire new models and algorithms whose realm of application will undoubtedly transcend disciplinary boundaries.

Nestedness in complex networks: Observation, emergence, and implications

2019-05-18 17:12:52

Manuel Sebastian Mariani, Zhuo-Ming Ren, Jordi Bascompte, Claudio Juan Tessone

http://dx.doi.org/10.1016/j.physrep.2019.04.001, http://arxiv.org/abs/1905.07593v1, http://arxiv.org/pdf/1905.07593v1

physics.soc-ph

th

The Sharing Economy (which includes Airbnb, Apple, Alibaba, Uber, WeWork, Ebay, Didi Chuxing, Amazon) blossomed across the world, triggered structural changes in industries and significantly affected international capital flows primarily by disobeying a wide variety of statutes and laws in many countries. They also illegally reduced and changing the nature of competition in many industries often to the detriment of social welfare. This article develops new dynamic pricing models for the SEOs and derives some stability properties of mixed games and dynamic algorithms which eliminate antitrust liability and also reduce deadweight losses, greed, Regret and GPS manipulation. The new dynamic pricing models contravene the Myerson Satterthwaite Impossibility Theorem.

Complexity, Stability Properties of Mixed Games and Dynamic Algorithms, and Learning in the Sharing Economy

2020-01-18 04:09:36

Michael C. Nwogugu

http://arxiv.org/abs/2001.08192v1, http://arxiv.org/pdf/2001.08192v1

cs.GT

th

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for {approximating} Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.

Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto

2020-06-12 22:53:18

Sam Ganzfried

http://arxiv.org/abs/2006.07443v5, http://arxiv.org/pdf/2006.07443v5

cs.GT

th

In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal-agent problem with moral hazard, \`a la Cvitani\'c, Possama\"i, and Touzi [27], while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray, Greenhalgh, Hu, Mao, and Pan [45] and Tornatore, Buccellato, and Vetro [88]. More precisely, to limit the spread of a virus, the population can decrease the transmission rate of the disease by reducing interactions between individuals. However, this effort, which cannot be perfectly monitored by the government, comes at social and monetary cost for the population. To mitigate this cost, and thus encourage the lockdown of the population, the government can put in place an incentive policy, in the form of a tax or subsidy. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. In terms of technical results, we demonstrate the optimal form of the tax, indexed on the proportion of infected individuals, as well as the optimal effort of the population, namely the transmission rate chosen in response to this tax. The government's optimisation problem then boils down to solving an Hamilton-Jacobi-Bellman equation. Numerical results confirm that if a tax policy is implemented, the population is encouraged to significantly reduce its interactions. If the government also adjusts its testing policy, less effort is required on the population side, individuals can interact almost as usual, and the epidemic is largely contained by the targeted isolation of positively-tested individuals.

Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic

2020-09-01 17:36:28

Emma Hubert, Thibaut Mastrolia, Dylan Possamaï, Xavier Warin

http://dx.doi.org/10.1007/s00285-022-01736-0, http://arxiv.org/abs/2009.00484v2, http://arxiv.org/pdf/2009.00484v2

q-bio.PE

th

On-line firms deploy suites of software platforms, where each platform is designed to interact with users during a certain activity, such as browsing, chatting, socializing, emailing, driving, etc. The economic and incentive structure of this exchange, as well as its algorithmic nature, have not been explored to our knowledge. We model this interaction as a Stackelberg game between a Designer and one or more Agents. We model an Agent as a Markov chain whose states are activities; we assume that the Agent's utility is a linear function of the steady-state distribution of this chain. The Designer may design a platform for each of these activities/states; if a platform is adopted by the Agent, the transition probabilities of the Markov chain are affected, and so is the objective of the Agent. The Designer's utility is a linear function of the steady state probabilities of the accessible states minus the development cost of the platforms. The underlying optimization problem of the Agent -- how to choose the states for which to adopt the platform -- is an MDP. If this MDP has a simple yet plausible structure (the transition probabilities from one state to another only depend on the target state and the recurrent probability of the current state) the Agent's problem can be solved by a greedy algorithm. The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), is NP-hard to approximate within any finite ratio; however, the special case, while still NP-hard, has an FPTAS. These results generalize from a single Agent to a distribution of Agents with finite support, as well as to the setting where the Designer must find the best response to the existing strategies of other Designers. We discuss other implications of our results and directions of future research.

The Platform Design Problem

2020-09-14 02:53:19

Christos Papadimitriou, Kiran Vodrahalli, Mihalis Yannakakis

http://arxiv.org/abs/2009.06117v2, http://arxiv.org/pdf/2009.06117v2

cs.GT

th

After the first lockdown in response to the COVID-19 outbreak, many countries faced difficulties in balancing infection control with economics. Due to limited prior knowledge, economists began researching this issue using cost-benefit analysis and found that infection control processes significantly affect economic efficiency. A UK study used economic parameters to numerically demonstrate an optimal balance in the process, including keeping the infected population stationary. However, universally applicable knowledge, which is indispensable for the guiding principles of infection control, has not yet been clearly developed because of the methodological limitations of simulation studies. Here, we propose a simple model and theoretically prove the universal result of economic irreversibility by applying the idea of thermodynamics to pandemic control. This means that delaying infection control measures is more expensive than implementing infection control measures early while keeping infected populations stationary. This implies that once the infected population increases, society cannot return to its previous state without extra expenditures. This universal result is analytically obtained by focusing on the infection-spreading phase of pandemics, and is applicable not just to COVID-19, regardless of "herd immunity." It also confirms the numerical observation of stationary infected populations in its optimally efficient process. Our findings suggest that economic irreversibility is a guiding principle for balancing infection control with economic effects.

Economic irreversibility in pandemic control processes: Rigorous modeling of delayed countermeasures and consequential cost increases

2020-10-01 14:28:45

Tsuyoshi Hondou

http://dx.doi.org/10.7566/JPSJ.90.114007, http://arxiv.org/abs/2010.00305v9, http://arxiv.org/pdf/2010.00305v9

q-bio.PE

th

Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.

Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model

2020-12-24 00:24:06

Gaia Belardinelli, Rasmus K. Rendsvig

http://dx.doi.org/10.1007/978-3-030-65840-3_3, http://arxiv.org/abs/2012.12982v1, http://arxiv.org/pdf/2012.12982v1

cs.AI