I will present some basic concepts and tools of the theory of stochastic processes, starting from discrete-time (stochastic) control theory and game theory. Also, I will present the main open problem in discrete-time stochastic games: whether every stochastic game with finitely many players (N>2), states, and actions, has a uniform equilibrium payoff.

Then I will motivate the continuous-time models making the connection between stochastic control and games with partial differential equations. I will end the talk with a presentation of asymptotic analysis of many-player games using the concept of mean-field games introduced by Pierre-Louis Lions and Jean-Michel Lasry (2006). Speaker(s): Asaf Cohen (Michigan)