Exponential Families and Game Dynamics

Abstract

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (a_ij). When two players choose strategies i and j the payoffs are a_ij and a_ji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.