Strategic Control of Myopic Best Reply in Repeated Games

Strategic Control of Myopic Best Reply in Repeated Games∗

How can a rational player strategically control a myopic best reply player in a repeated two-player game? We show that in games with strategic substitutes or strategic complements the optimal control strategy is monotone in the initial action of the opponent, in time periods, and in the discount rate. As an interesting example outside this class of games we present a repeated “textbook-like” Co...

Best-reply matching in games

We study a new equilibrium concept in non-cooperative games, where players follow a behavioral rule called best-reply matching. Under this rule a player matches the probability of playing a pure strategy to the probability that this strategy is a best reply. Kosfeld, Droste, and Voorneveld (2001) show that best-reply matching equilibria are stationary states in a simple model of social learning...

Strategic complexity in repeated extensive games

This paper studies a machine (finite automaton) game for a two-player extensive-form stage game. We introduce a new measure ofstrategic complexity called “multiple complexity”, which considers in-formation structure inside the stage games as well as the number ofstates of machines. In contrast to Piccione and Rubinstein (1993),we prove existence of non-static equilibria....

Leading Best-Response Strategies in Repeated Games

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...