Qualitative Concurrent Stochastic Games with Imperfect Information

TL;DR

This paper analyzes a complex model of concurrent stochastic games with imperfect information, proving the computational complexity of almost-sure winning strategies and characterizing the strategies required for the first player.

Contribution

It introduces a formal model combining concurrency, imperfect information, and stochasticity, and establishes 2-ExpTime completeness for the almost-sure winning strategy problem.

Findings

Deciding almost-sure winning strategies is 2-ExpTime complete.

Characterization of strategies needed for almost-sure winning.

Formalization of a new game model with concurrency, imperfect info, and stochasticity.

Abstract

We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability distribution depending on the previous state and on the pair of actions chosen by the players. Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs. Therefore, if two partial plays are indistinguishable by some player, he should behave the same in both of them. We consider reachability (does the play eventually visit a final state?) and B\"uchi objective (does the play visit infinitely often a final state?). Our main contribution is to prove that the following problem is complete for 2-ExpTime: decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her oponent. We also characterise those strategies needed by the first player to almost-surely win.