Three More Classes of Games with the Fictitious Play Property

Fictitious play is the oldest and most studied learning process for games. Since Robinson’s (1951) classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for some important classes of games, most notably 2×2 games (Miyazawa, 1961), weighted potential games (Monderer and Shapley, 1996), and supermodular games with diminishing returns (Krishna, 1992). We extend all three of these results, establishing convergence for 2×m games, for ordinal potential games, and for quasi-supermodular games with diminishing returns. Journal of Economic Literature classification numbers: C72, D83.