  The literature explores many different variations on this theme. One can restrict how many past trials the player remembers or how much weight the player places upon older trials. One can embed the player in a large population and restrict how much a player knows about interactions within that population. One can introduce a “neighborhood structure,” so that players interact only with their neighbors. One can introduce a stochastic element. For instance, building on work of M. I. Friedlin and A. D. Wentzell (1984) and Michihiro Kandori, George Mailath, and Rafael Rob (1993), H. Peyton Young (1993, 1996, 1998) develops a model of how conventions evolve in which each player chooses a “best reply” with probability \(1-\varepsilon\) and some random strategy with probability \(\varepsilon\). One can also generalize the fictitious play framework to accommodate correlated equilibrium. Peter Vanderschraaf (2001) explores a variant of fictitious play in which a player frames hypotheses about correlations between her opponents’ strategies and external events. Applying this framework to convention, he argues that we can treat the emergence of correlated equilibrium conventions as an instance of rational belief-fixation through inductive deliberation.