Building Stable Conventions: heterogeneity in choice rules

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Strategies of players in a population are updated according to the choice rules of agents, where each agent is a player or a coalition of players. It is shown that choice rules that satisfy a specific type of asymmetry can be combined in a variety of ways while retaining this asymmetry. It is known that, at a global level, this asymmetry implies stochastic stability of a given homogeneous strategy profile. Taken together, these results enable two approaches, one reductive, the other constructive. Firstly, for models in which every agent follows the same choice rule, stochastic stability can be proven by showing that the asymmetry holds for a representative agent. This allows us to easily recover and extend many results from the literature. Secondly, agents who follow choice rules that satisfy the asymmetry can be combined arbitrarily while the same homogeneous strategy profile remains stochastically stable.