The limit set of perfect public equilibrium payoffs of a repeated game as the discount factor goes to one is characterized, with examples, even when the full-dimensionality condition fails.

Stochastic fictitious play (SFP) assumes that agents do not try to influence the future play of their current opponents, an assumption that is justified by appeal to a setting with a large population of players who are randomly matched to play the game. However, the dynamics of SFP have only...