Coevolution of strategies and update rules in the Prisoner's Dilemma game on complex networks

TL;DR

This paper investigates how co-evolving strategies and update rules in the Prisoner's Dilemma on complex networks influence cooperation, showing that co-evolution generally promotes higher cooperation levels across various network topologies.

Contribution

It introduces a co-evolutionary model of strategies and update rules in the Prisoner's Dilemma on complex networks, highlighting the emergence of replicator dynamics and increased cooperation.

Findings

Heterogeneous networks favor cooperation through co-evolution.

Replicator dynamics is often the preferred update rule after co-evolution.

Co-evolution leads to higher cooperation levels compared to fixed update rules.

Abstract

In this work we study a weak Prisoner\^as Dilemma game in which both strategies and update rules are subjected to evolutionary pressure. Interactions among agents are specified by complex topologies, and we consider both homogeneous and heterogeneous situations. We consider deterministic and stochastic update rules for the strategies, which in turn may consider single links or full context when selecting agents to copy from. Our results indicate that the co-evolutionary process preserves heterogeneous networks as a suitable framework for the emergence of cooperation. Furthermore, on those networks, the update rule leading to a larger fraction, which we call replicator dynamics, is selected during co-evolution. On homogeneous networks we observe that even if replicator dynamics turns out again to be the selected update rule, the cooperation level is larger than on a fixed update rule framework. We conclude that for a variety of topologies, the fact that the dynamics coevolves with the strategies leads in general to more cooperation in the weak Prisoner's Dilemma game.