One against All in the Fictitious Play Process

There are only few "positive" results concerning multi-person games with the fictitious play property, that is, games in which every fictitious play process approaches the set of equilibria. In this paper we characterize classes of multi-person games with the fictitious play property. We consider an (n+1) player game {0,1,2,....,n} based on n two-person sub-games. In each of these sub-games player 0 plays against one of the other players. Player 0 is regulated, so that he must choose the same strategy in all n sub-games. We show that if all sub-games are either zero-sum games, weighted potential games, or games with identical payoff functions, then the fictitious play property holds for the associated game.