Optimal Strategies in Perfect-Information Stochastic Games with Tail Winning Conditions

We prove that optimal strategies exist in every perfect-information stochastic game with finitely many states and actions and a tail winning condition.

Solving Simple Stochastic Games with Few Random Vertices

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The permutation-enumeration algorithm performs an exhaustive search among these strategies, while the permutation-improvement algorithm is based on successive improvements, `a la Hoffman-Karp. Our algorithms improve previously known algorithms in several aspects. First they run in polynomial time when the number of random vertices is fixed, so the problem of solving simple stochastic games is fixed-parameter tractable when the parameter is the number of random vertices. Furthermore, our algorithms do not require the input game to be transformed into a stopping game. Finally, the permutation-enumeration algorithm does not use linear programming, while the permutation-improvement algorithm may run in polynomial time.

Determinacy and Decidability of Reachability Games with Partial Observation on Both Sides

We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions.