The Effect of a Random Drift on Mixed and Pure Strategies in the Snowdrift Game

TL;DR

This paper demonstrates that in the Snowdrift Game, introducing a small amount of noise in the replicator dynamics allows mixed strategists to invade populations of pure strategists, challenging the usual equivalence assumption.

Contribution

It reveals that even minimal noise can break the equivalence between pure and mixed strategies in evolutionary dynamics.

Findings

Mixed strategists can invade pure populations with noise

Pure and mixed strategies are not always equivalent under stochastic effects

Small noise influences stability and invasion dynamics in the Snowdrift Game

Abstract

The replicator dynamics of players choosing either mixed or pure strategies are usually regarded as equivalent, as long as strategies are played with identical frequencies. In this paper we show that a population of pure strategists can be invaded by mixed strategists in any two-player game with equilibrium coexistence upon the addition of an arbitrarily small amount of noise in the replication process.