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, à 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.
simple stochastic games, algorithm
2-person games (msc 91A05), Stochastic games (msc 91A15)
Logistics (theme 3)
Int. Fed. of Computational Logic
Logical Methods in Computer Science
Networks and Optimization

Gimbert, H, & Horn, F. (2009). Solving Simple Stochastic Games with Few Random Vertices. Logical Methods in Computer Science, 5(2).