Fictitious Play

A process by which players assume that the strategies of their opponents are randomly chosen from some unknown stationary distribution. In each period, a player selects her best response to the historical frequency of actions of her opponents. The process was first noted by Julia Robinson who also noted that the process converges to the equilibrium for two-player zero sum games. While the process does not always converge in other settings, it is known that if it converges, then the point of convergence is a Nash equilibrium of the game. updated: 15 August 2005