Evolutionary dynamics, intrinsic noise and cycles of co-operation

TL;DR

This paper analytically investigates how demographic noise can induce coherent oscillations between cooperation and defection in finite populations playing the prisoner's dilemma, extending to strategies with errors.

Contribution

It provides a systematic analytical framework to characterize noise-induced cycles in evolutionary game dynamics, including complex eigenvalue regimes and different microscopic dynamics.

Findings

Demographic noise can amplify to produce oscillations in cooperation levels.

Analytical predictions match observed quasi-cycles in simulations.

Extended analysis includes strategies with error-prone decision-making.

Abstract

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues. These quasi-cycles between co-operation and defection have previously been observed in computer simulations; here we provide a systematic and comprehensive analytical characterization of their properties. We are able to predict their power spectra as a function of the mutation rate and other model parameters, and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics. We also extend our analysis to the iterated prisoner's dilemma game with a win-stay lose-shift strategy, appropriate in situations where players are subject to errors of the trembling-hand type.