Dynamics for Infinite Dimensional Games

The explosion of interest amongst game-theorists in recent years in the ‘evolutionary’ (learning) dynamics of repeated games, has generally been concerned with 2-player (usually symmetric) games in which each player has available a finite number of pure strategies. The learning dynamics of players chosen from large, usually infinite, populations of such players, are then taken to describe the evolution of the probability with which a randomly chosen player will play a given pure strategy. In a suitable continuous-time limit, in which the game is repeated continuously, these dynamics take the form of a finite-dimensional system of differential equations. Various versions of these dynamics have been extensively studied in various game-theoretic contexts, and up-to-date accounts of much of the recent research in this area can be found in Weibull (1996), Samuelson (1997) and Hofbauer and Sigmund (1999).