Prisoner's dilemma on directed networks

TL;DR

This paper investigates the prisoner's dilemma game on directed networks using a pair mean-field approximation and simulations, analyzing how noise, temptation, and network structure influence cooperation.

Contribution

It introduces a heterogeneous pair mean-field approach for directed networks and provides analytical predictions for critical temptation thresholds.

Findings

Good agreement between theory and simulations in high noise regime

Phase diagrams depend on temptation, noise, and network degree

Comparison with non-directed networks highlights structural effects

Abstract

We study the prisoner's dilemma model with a noisy imitation evolutionary dynamics on directed out-homogeneous and uncorrelated directed random networks. An heterogeneous pair mean-field approximation is presented showing good agreement with Monte Carlo simulations in the limit of weak selection (high noise) where we obtain analytical predictions for the critical temptations. We discuss the phase diagram as a function of temptation, intensity of noise and coordination number of the networks and we consider both the model with and without self-interaction. We compare our results with available results for non-directed lattices and networks.