Evolutionary game dynamics in finite populations

Christine Taylor,M Nowak,A Sasaki,D Fudenberg

doi:10.1016/j.bulm.2004.03.004

Christine Taylor, M Nowak + Show 2 more

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https://doi.org/10.1016/j.bulm.2004.03.004

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Abstract

We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.

Highlights

In this paper, we study evolutionary dynamics of a game with two strategies A and B
The payoff matrix for the game is AB Aa b Bc d Strategy A player receives payoff a when playing against another strategy A player, and payoff c when playing against a strategy B player
We focus on analytic results for explicit stochastic process, as opposed to simulations or equilibrium definitions, and uncover interesting selection phenomena for finite population size that do not exist in the infinite limit

Summary

Introduction

We study evolutionary dynamics of a game with two strategies A and B. The payoff matrix for the game is AB Aa b Bc d Strategy A player receives payoff a when playing against another strategy A player, and payoff c when playing against a strategy B player. A strategy B player would receive payoffs b and d when playing against A and B players, respectively. We denote by xA and xB the frequency of individuals adopting strategy A and B respectively. The fitness of A and B players are

Corresponding Author

A Frequency Dependent Moran Process

Selection Dynamics in Finite Populations

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Conclusions