| Abstract: |
| I will present a non-asymptotic approach to quantifying the gap between different notions of equilibrium in stochastic differential games with many players. Under suitable semi-monotonicity conditions, one can derive estimates for the Nash and Pontryagin systems that are uniform in the number of players. These estimates, in turn, yield quantitative convergence results for open-loop and closed-loop equilibria when interactions between players are weak. The results apply to games with interactions that are not necessarily symmetric and possibly much sparser than in classic mean field game theory, and they confirm the universality of the mean field game limit for games governed by sufficiently dense networks. Based on a joint work with Marco Cirant (Padua) and Joe Jackson (Chicago). |
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