Ergodic Problems in Differential Games

Abstract

We present and study a notion of ergodicity for deterministic zero-sum differential games that extends the one in classical ergodic control theory to systems with two conflicting controllers.We show its connections with the existence of a constant and uniform long-time limit of the value function of finite horizon games, and characterize this property in terms of Hamilton-Jacobi-Isaacs equations.We also give several sufficient conditions for ergodicity and describe some extensions of the theory to stochastic differential games.

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