Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner's dilemma games

TL;DR

This paper investigates how the difference between interaction and learning neighborhoods in a layered network influences cooperation in evolutionary prisoner's dilemma games, revealing a resonance-like effect.

Contribution

It introduces a layered graph model with separate interaction and learning networks and analyzes their impact on cooperation using simulations and analytical methods.

Findings

Cooperation exhibits a resonance-like behavior as the number of learning edges increases.

Analytical results match the Monte Carlo simulations.

Layered network structure significantly affects cooperation dynamics.

Abstract

We study an evolutionary prisoner's dilemma game with two layered graphs, where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption (learning) mechanism. This system is investigated by means of Monte Carlo simulations and an extended pair-approximation method. We consider the average density of cooperators in the stationary state for a fixed interaction graph, while varying the number of edges in the learning graph. According to the Monte Carlo simulations, the cooperation is modified substantially in a way resembling a coherence-resonance-like behavior when the number of learning edges is increased. This behavior is reproduced by the analytical results.