Making new connections towards cooperation in the prisoner's dilemma game

TL;DR

This paper investigates how allowing players in the prisoner's dilemma to form new connections based on success can promote cooperation, leading to heterogeneous networks with optimal connectivity for cooperation.

Contribution

It introduces a coevolutionary rule where successful players can extend their networks, shifting the cooperation survival threshold and revealing an optimal degree for cooperation.

Findings

Heterogeneous networks emerge with exponential degree distributions.

An optimal maximal degree enhances cooperation.

Cooperation survives at higher temptation levels with network extension.

Abstract

Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new connections and thus permanently extend their neighborhoods, provided they have been successful in passing their strategy to the opponents. We show that this simple coevolutionary rule shifts the survival barrier of cooperators towards high temptations to defect and results in highly heterogeneous interaction networks with an exponential fit best characterizing their degree distributions. In particular, there exist an optimal maximal degree for the promotion of cooperation, warranting the best exchange of information between influential players.