A Weakend Form of Fictitious Play in Two-Person Zero-Sum Games
Ben B. van der Genugten · Data Archiving and Networked Services (DANS) · 1998
Fictitious play can be seen as a numeric iteration procedure for determining the value of a game and corresponding optimal strategies.Although convergence is slow, it needs only a modest computer storage.Therefore it seems to be a good way out for analyzing large games.In this paper we consider a weakened form of …ctitious play, which can be interpreted that players at each stage do not have to make the best choice against the total of past choices of the other player but only an increasingly better one.Theoretical bounds for convergence are derived.Furthermore it is shown that this new form can speed up convergence considerably in practice.The method is related to generalizations in which the game matrix itself becomes better known as the number of stages increases.Finally, the convergence of the strategies themselves is discussed.AMS 1991 subject classi…cation.Primary 90D05, 90D10.