Criticality and Griffiths phases in random games with quenched disorder

TL;DR

This paper investigates how quenched disorder in payoffs affects the critical dynamics of evolutionary games, revealing the emergence of Griffiths phases characterized by slow, power-law decay of cooperation and defection.

Contribution

It extends understanding of disorder effects by demonstrating the presence of Griffiths phases in random evolutionary games with quenched payoff fluctuations.

Findings

Payoff heterogeneity promotes cooperation in competitive scenarios.

Quenched disorder induces Griffiths phases with slow, power-law decay.

Symmetric Griffiths phase observed near defector extinction point.

Abstract

The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte-Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.