Markov Perfect Equilibria in discrete finite-player and mean-field games

We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Through the Kuramoto mean-field game, we investigate the emergence of multiple self-organizing equilibria with complex time-dependent dynamics. This is in contrast to continuous-time finite-player games, which admit unique MPE in the absence of monotonicity conditions. While discrete-time problems generally do not admit unique MPE, we show that uniqueness is remarkably recovered when the time steps are small. This result, established without relying on any monotonicity conditions, underscores the importance of inertia in dynamic games. Finally, we discuss different learning algorithms and prove their convergence to the unique MPE. This is joint work with Mathieu Laurière, Mete Soner, Qinxin Yan, and Atilla Yilmaz.