An N-player sequential stochastic game with identical payoffs

A sequential stochastic game among an arbitrary number of players in which all players´ payoffs are identical is analyzed. The players are unaware that they are in a game and hence they have no knowledge of other players´ strategies or the payoff structure. At each instant the players use a simple learning algorithm to update their mixed strategy choices based entirely on the response of a random environment. It is shown that the expected change in each player´s payoff is nonnegative at every instant, so that the group improves its performance monotonically. This result appears to have important implications in decentralized decision-making in large complex systems.