A homoclinic route to asymptotic full cooperation in adaptive networks and its failure

TL;DR

This paper explores how adaptive networks can evolve towards full cooperation through intrinsic dynamics, but also highlights how such cooperation can fail in finite systems due to episodic defection.

Contribution

It introduces a dynamical mechanism that can lead to asymptotic full cooperation in adaptive networks, and analyzes its failure modes in finite systems.

Findings

Full cooperation can emerge asymptotically in adaptive networks.

Finite systems exhibit long cooperation periods interrupted by defection episodes.

Systemic failure of cooperation can occur due to these episodic defection events.

Abstract

We consider the evolutionary dynamics of a cooperative game on an adaptive network, where the strategies of agents (cooperation or defection) feed back on their local interaction topology. While mutual cooperation is the social optimum, unilateral defection yields a higher payoff and undermines the evolution of cooperation. Although no a priori advantage is given to cooperators, an intrinsic dynamical mechanism can lead asymptotically to a state of full cooperation. In finite systems, this state is characterized by long periods of strong cooperation interrupted by sudden episodes of predominant defection, suggesting a possible mechanism for the systemic failure of cooperation in real-world systems.