A myopic adjustment process leading to best-reply matching

We analyze a myopic strategy adjustment process in strategic-form games. It is shown that the steady states of the continuous time limit, which is constructed assuming frequent play and slow adjustment of strategies, are exactly the best-reply matching equilibria, as discussed by Droste, Kosfeld, and Voorneveld (2000. Mimeo, Tilburg University). In a best-reply matching equilibrium every player ‘matches’ the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure-strategy profile played by his opponents. We derive stability results for the steady states of the continuous time limit in 2×2 bimatrix games and coordination games. Analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game. Moreover, absorbing states of the process correspond to best-reply matching equilibria of the game.