Replicator dynamics with turnover of players

Evolution of mean strategy and payoff in the game 'matching pennies' with turnover of players.

By Jeppe Juul, Ardeshir Kianercy, Sebastian Bernhardsson, and Simone Pigolotti.

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.

The article can be found here.