Learning of equilibria by a population with minimal information

Abstract

In an evolutionary game context, we consider a population of players endlessly repeating a game, each player selecting a strategy at each time point to play against the rest of the population. Roughly stated, a given player switches strategy at random intervals according to two rules, 1. (i) The probability of switching over a short time interval is proportional to the gap between the player's current payoff and the highest payoff currently possible, 2. (ii) When a player does switch, she chooses a new strategy at random, with equal probabilities, among all other strategies. Thus, in contrast to most evolutionary game models, adaptation in this model is neither a best response nor an imitative response. The simple switching rules are meant to characterize a minimally informed and minimally calculating population. The main result is that the dynamics of the model will, for a sizable class of payoff structures, find a Nash equilibrium when best reply dynamics would not.