Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-Positional

Hugo Gimbert (1) , Edon Kelmendi (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a payoff function which associates to each infinite sequence of states and actions a real number. We prove that if the 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 equilibria in shift-invariant games, a second contribution of the paper.

Mots clés: stochastic games

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

Hugo Gimbert, Edon Kelmendi. Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-Positional. 2014. ⟨hal-00936371v2⟩