Replicator dynamics with turnover of players

Abstract: We study adaptive dynamics in games where players abandon the population at a given rate, and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such process leads macroscopically to a variant of the replicator equation, with an additional term accounting for player turnover. We study how Nash equilibria and the dynamics of the system are modified by this additional term, for prototypical examples such as the rock-scissor-paper game and different classes of two-action games played between two distinct populations. We conclude by showing how player turnover can account for non-trivial departures from Nash equilibria observed in data from lowest unique bid auctions.