Comparison of algorithms for simple stochastic games

Simple stochastic games are turn-based 21/2-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms - value iteration, strategy iteration and quadratic programming - both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISMgames 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games.