On the effect of memory on the Prisoner's Dilemma game in correlated networks

TL;DR

This paper investigates how memory affects cooperation in the Prisoner's Dilemma game played on various correlated networks, revealing that memory can reduce the influence of network structure and that assortativity enhances cooperation under high temptation to defect.

Contribution

It provides a detailed simulation study on the impact of memory in cooperation dynamics within correlated networks, an area not well understood before.

Findings

Memory decreases the influence of network structure on cooperation.

Assortativity improves cooperation when temptation to defect is high.

Network type affects the evolution of cooperation in the presence of memory.

Abstract

Game theory is fundamental to understanding cooperation between agents. Mainly, the Prisoner's Dilemma is a well-known model that has been extensively studied in complex networks. However, although the emergence of cooperation has been investigated before, the influence of memory in its evolution is not well understood. This paper presents a detailed study of cooperation dynamics in which agents have memory. We simulate the evolutionary Prisoner's dilemma game on random, scale-free and networks presenting degree-degree correlation. Through extensive simulations, we show that assortativity can improve cooperation when the temptation to defect increases. Moreover, we show that the inclusion of memory decreases the network structure influence. Our results contribute to understanding the role of the network structure and the player's memory of cooperation.