Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs

TL;DR

This paper investigates how fluctuating payoffs in evolutionary games influence dynamics, revealing unfair coexistence and unexpected strategy reversals caused by environmental variability.

Contribution

It introduces a framework to analyze the effects of arbitrary temporal payoff variations on evolutionary game outcomes, highlighting novel unfair and anomalous behaviors.

Findings

Unfair coexistence of strategies due to payoff fluctuations

Anomalous coexistence in Prisoner's Dilemma

Selection reversal in Hawk-Dove game

Abstract

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair", meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the Prisoner's Dilemma, and an unexpected selection reversal in the Hawk-Dove game.