text: 77,77,1349354924639997955,2880029134,Marco Pangallo,"In <LINK> we showed that reaching equilibrium in 2-player games could be difficult. In our new paper, <LINK>, we do lots of maths and show that it is even more difficult in games with many players, unless players best-respond in a random order! <LINK> This has been my first paper more on the coordination side, and can't thank enough @mungoluca, Sam Wiese and Yoojin Jang for all their work during summer internships! And of course also @TorstenHeinriX, Bassel and Alex for their key contributions!",https://arxiv.org/abs/2101.04222,"We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games. ","Best-response dynamics, playing sequences, and convergence to