Reachability and Safety Games with Strategy Improvement

This paper is about two-player infinite stochastic games with imperfect information. We first study on determinacy (optimal value) and optimal (-optimal) strategies in reachability games. The main concern here is to give simple expressions of a value of the game. We provide an alternative prove in showing the existence of memoryless mixed -optimal strategy for Player I in any reachability games. We then investigate the existence of optimal (-optimal) strategies for each player in a duality of reachability games, namely a safety game. The result of safety game is exactly a dual problem of reachability