Fictitious Play - Terminology

Terminology

Berger (2007) states that "what modern game theorists describe as "fictitious play" is not the learning process that George W. Brown defined in his 1951 paper. Brown's original version differs in a subtle detail..." and points out that modern usage involves the players updating their beliefs simultaneously. Berger goes on to say that Brown clearly states that the players update alternatingly. Berger then uses Brown's original form to present a simple and intuitive proof of convergence in the case of nondegenerate ordinal potential games.

The term "fictitious" had earlier been given another meaning in game theory. Von Neumann and Morgenstern defined a "fictitious player" as a player with only one strategy, added to an n-player game to turn it into a n+1-player zero-sum game.