Probabilistic limit theory for mean field games

Probabilistic limit theory for mean field games

###### Probability Seminar

#### Dan Lacker (Columbia University)

**Thursday, February 8, 2018 -3:15pm to 4:15pm**

Mean field game theory describes continuum limits of symmetric large-population games. These games can often be seen as competitive extensions of classical models of interacting particle systems, where the particles are now "controlled state process" (with application-specific interpretation, such as position, income, wealth, etc.). The coupled optimization problems faced by each process are typically resolved by Nash equilibrium, and there is a large and growing literature on solvability problems (both theoretical and computational). On the other hand, relatively little is known on how to rigorously pass from a finite population to a continuum, especially for dynamic stochastic games. The basic question is: Given for each N a Nash equilibrium for the N-player game, do the equilibria (more precisely, the empirical distributions of state processes) converge as N tends to infinity? This talk is an overview of the known probabilistic limit theorems in this context (law of large numbers, fluctuations, and large deviations), the ideas behind them, and some open problems.