- Abstract We present a new algorithm for polynomial time learning of near optimal behavior in stochastic games. This algorithm incorporates and integrates important recent results of Kearns and Singh 1998] in reinforcement learning and of Monderer and Tennenholtz 1997] in repeated games. In stochastic games we face an exploration vs. exploitation dilemma more complex than in Markov decision processes. Namely, given information about particular parts of a game matrix, how much e ort should the agent invest in learning its unknown parts. We explain and address these issues within the class of single controller stochastic games. This solution can be extended to stochastic games in general.