Replicator dynamics with turnover of players

TL;DR

This paper extends the replicator dynamics model to include player turnover, analyzing its impact on equilibrium stability and dynamics, with applications to game theory and auction data.

Contribution

It introduces a modified replicator equation incorporating player turnover and explores its effects on game equilibria and dynamics.

Findings

Turnover alters stability of Nash equilibria.

Modified dynamics explain deviations from Nash in auction data.

Player turnover leads to non-trivial equilibrium outcomes.

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.