An adjusted payoff-based procedure for normal form games

Mario Bravo (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study a simple adaptive model in the framework of an $N$-player normal form game. The model consists of a repeated game where the players only know their own strategy space and their own payoff scored at each stage. The information about the other agents (actions and payoffs) is unknown. In particular, we consider a variation of the procedure studied by Cominetti et al. (2010) where, in our case, each player is allowed to use the number of times she has played each action to update her strategy. The resultant stochastic process is analyzed via the so-called ODE method from stochastic approximation theory. We are interested in the convergence of the process to rest points of a related continuous dynamics. Results concerning almost sure convergence and convergence with positive probability are obtained and applied to a traffic game. Also, we provide some examples where convergence occurs with probability zero. Finally, we verify that part of the analysis holds when players are facing a random environment.

Mots clés: Normal form games; Learning; Adaptive dynamics; Stochastic approximation

Domaines: Informatique et théorie des jeux [cs.GT]; Probabilités [math.PR]

Mario Bravo. An adjusted payoff-based procedure for normal form games. 2011. ⟨hal-00603852⟩