Large Population Limits for Evolutionary Dynamics with Random Matching

A frequent assumption in evolutionary game theory is that the population size is sufficiently large so that matching of players is essentially deterministic and payoffs are determined by the expected value of a random match. This paper studies the assumption in the context of a well known model of Kandori, Malaith, and Rob. As the population size tends to infinity, the stationary distribution of an evolutionary process defined by a class of two strategy–two player games with random matching of players fails to converge to the stationary distribution of the same process with the random match replaced by its expected value.