Co-evolutionary games on networks

TL;DR

This paper investigates co-evolutionary games on networks, revealing how stationary Nash equilibria are disrupted and reestablished through avalanche dynamics, with scale-free distributions indicating critical behavior across various game variants.

Contribution

It demonstrates the emergence of scale-free avalanche distributions in co-evolutionary network games and links these to Nash equilibria and phase transitions in the system.

Findings

Avalanche size distributions follow a scale-free pattern.

Transition from subcritical to critical dynamics correlates with macrostate degeneracy.

Critical behavior observed across multiple game variants.

Abstract

We study agents on a network playing an iterated Prisoner's dilemma against their neighbors. The resulting spatially extended co-evolutionary game exhibits stationary states which are Nash equilibria. After perturbation of these equilibria, avalanches of mutations reestablish a stationary state. Scale-free avalanche distributions are observed that are in accordance with calculations from the Nash equilibria and a confined branching process. The transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game.