Submixing and shift-invariant stochastic games

Abstract We study optimal strategies in two-player stochastic games that are played on a finite graph, equipped with general payoff function. The existence of do not make use memory and randomisation is desirable property vastly simplifies the algorithmic analysis such games. Our main theorem gives sufficient condition for maximizer to possess simple strategy. imposed function, saying does depend any prefix (shift-invariant) combining two trajectories give higher than parts (submixing). core technical enables proof $$\epsilon$$ ϵ -subgame-perfect when function shift-invariant. Furthermore, same techniques can be used prove finite-memory transfer-type theorem: namely shift-invariant submixing functions, one-player minimizer implies show numerous classical functions