Approximation of Large Dynamic Games

We provide a framework for simplifying the analysis and estimation of dynamic games with many agents by using nonatomic limit game approximations. We show that that the equilibria of a nonatomic approximation are epsilon-Bayesian-Nash Equilibria of the dynamic game with many players if the limit game is continuous. We also provide conditions under which the Bayesian-Nash equilibrium strategy correspondence of a large dynamic game is upper hemicontinuous in the number of agents. We use our results to show that repeated static Nash equilibria are the only equilibria of continuous repeated games of imperfect public or private monitoring in the limit as N approaches innity. Extensions include: games with large players in the limit as N approaches innity; games with (discontinuous) entry and exit decisions; Markov perfect equilibria of complete information stochastic games with aggregate shocks; and games with private and/or imperfect monitoring. Finally we provide an application of our framework to the analysis of large dynamic auction platforms such as E-Bay using the nonatomic limit model of Satterthwaite and Shneyerov [33].

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