Learning algorithms for repeated bimatrix Nash games with incomplete information

The purpose of this paper is to study a particular recursive scheme for updating the actions of two players involved in a Nash game, who do not know the parameters of the game, so that the resulting costs and strategies converge to (or approach a neighborhood of) those that could be calculated in the known parameter case. We study this problem in the context of a matrix Nash game, where the elements of the matrices are unknown to both players. The essence of the contribution of this paper is twofold. On the one hand, it shows that learning algorithms which are known to work for zero-sum games or team problems can also perform well for Nash games. On the other hand, it shows that, if two players act without even knowing that they are involved in a game, but merely thinking that they try to maximize their output using the learning algorithm proposed, they end up being in Nash equilibrium.This research was supported in part by NSF Grant No. ECS-87-14777.