Evolutionary Prisoner's Dilemma game on the Newman-Watts networks

TL;DR

This paper investigates how adding extra links to a one-dimensional chain affects cooperation dynamics in an evolutionary Prisoner's Dilemma game, using simulations and theoretical analysis.

Contribution

It introduces a study of cooperation on Newman-Watts networks, combining Monte Carlo simulations and dynamical mean-field theory to analyze phase transitions.

Findings

Connectivity extension alters the phase diagram significantly.

Noise level influences cooperation stability.

Network topology impacts evolutionary game outcomes.

Abstract

Maintenance of cooperation was studied for a two-strategy evolutionary Prisoner's Dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest and next-nearest neighbor interactions. The applied host geometry makes possible to study the impacts of two conflicting topological features. The evolutionary rule involves some noise affecting the strategy adoptions between the interacting players. Using Monte Carlo simulations and the extended versions of dynamical mean-field theory we determined the phase diagram as a function of noise level and a payoff parameter. The peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by Newman and Watts.