Ergodic Problems in Differential Games
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.
KeywordsDifferential Game Stochastic Game Cell Problem Dynamic Programming Principle Stochastic Differential Game
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