Minimal Inclusive Sets in Special Classes of Games
A companion paper, Sanchirico (1996), provides a probabilistic theory of learning in games with the convergence property that, almost surely, play will remain almost always (i.e., forever after some point) within one of the stage game's "minimal inclusive sets." This paper investigates the size of minimal inclusive sets in several classes of games, notably, those for which other learning processes have been shown to converge (in various manners weaker than convergence of actual play). These include certain supermodular games, congestion games, potential games, games with identical interests, and games with bandwagon effects. It is shown that in all these classes, if all of a game's pure equilibria are strict (a fortiori, if its payoffs are generic), then all of its minimal inclusive sets will be singletons consisting of Nash equilibria.
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