Submixing and Shift-invariant Stochastic Games

Hugo Gimbert (1) , Edon Kelmendi (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 University of Oxford

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the payoff function is both shift-invariant and submixing, then the game is half-positional, i.e. the first player has an optimal strategy which is both deterministic and stationary. This result relies on the existence of epsilon-subgame-perfect strategies in shift-invariant games, a second contribution of the paper. The techniques can be used to establish a third result: for shift-invariant and submixing payoff functions, the existence of finite-memory strategies for player 2 in one-player games implies the same property for two-player games as well.

Mots clés: stochastic games

Domaines: Informatique et théorie des jeux [cs.GT]

Hugo Gimbert, Edon Kelmendi. Submixing and Shift-invariant Stochastic Games. 2014. ⟨hal-00936371v4⟩