Blackwell-Optimal Strategies in Priority Mean-Payoff Games

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes

Applying Blackwell optimality: priority mean-payoff games as limits of multi-discounted game

International audienceWe define and examine priority mean-payoff games - a natural extension of parity games. By adapting the notion of Blackwell optimality borrowed from the theory of Markov decision processes we show that priority mean-payoff games can be seen as a limit of special multi-discounted games

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

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

Playing in stochastic environment: from multi-armed bandits to two-player games

Given a zero-sum infinite game we examine the question if players have optimal memoryless deterministic strategies. It turns out that under some general conditions the problem for two-player games can be reduced to the same problem for one-player games which in turn can be reduced to a simpler related problem for multi-armed bandits

Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $\omega$-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy that achieves the energy-parity objective with probability $1$ when starting at a given energy level $k$, is decidable and in $NP \cap coNP$. The same holds for checking if such a $k$ exists and if a given $k$ is minimal