Evolutionary Games and Matching Rules

This study considers evolutionary models with non-uniformly random matching when interaction occurs in groups of n>=2 individuals. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy – and consequently long-run behavior in the population – varies with the frequencies of different group types. These frequencies crucially depend on the particular matching process at hand. Two new equilibrium concepts are introduced: Nash equilibrium under a matching rule (NEMR) and evolutionarily stable strategy under a matching rule (ESSMR). When matching is uniformly random, these reduce to Nash equilibrium and evolutionarily stable strategy, respectively. Several results that are known to hold for population games under uniform random matching carry through to our setting. In our most novel contribution, we derive results on the efficiency of the Nash equilibria of population games and show that for any (fixed) payoff structure, there always exists some matching rule leading to average fitness maximization in NEMR. Finally, we provide a series of applications to commonly studied normal-form games.