Seminar

Stochastic games played on a circle

Guillaume Vigeral (Université Paris Dauphine)

September 23, 2011, 13:45–15:00

Toulouse

Room MS 003

Decision Mathematics Seminar

Abstract

We consider some two-player zero-sum stochastic games played on the circle. At each stage the state of the game rotates by an angle depending on the actions played by both players. For some fixed length of the game n, the goal of the first player is to maximize the Cesaro mean of the payoffs obtained in the n first stages of the game, while the goal of the second player is to minimize the same quantity. We study the asymptotic behavior of the value of the n-stage game as the length n tends to infinity. We give sufficient conditions for convergence of the values, and also for ergodicity of the problem.