Calculus of Variations and Geometric Measure Theory

O. Alvarez - M. Bardi

Ergodic problems in differential games

created by bardi on 06 Sep 2007
modified on 01 Aug 2008


Published Paper

Inserted: 6 sep 2007
Last Updated: 1 aug 2008

Journal: Ann. Internat. Soc. Dynam. Games
Volume: 9
Pages: 131-152
Year: 2007

in " Advances in Dynamic Game Theory", S. Jorgensen et al. eds., pp. 131--152, Ann. Internat. Soc. Dynam. Games, 9, Birkh\"auser, Boston, 2007.


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.

Keywords: Hamilton-Jacobi-Isaacs equations, Ergodic control, differential games, controlled diffusion processes