Evolutionary prisoner's dilemma game on hierarchical lattices

TL;DR

This study investigates how hierarchical lattice structures influence cooperation in evolutionary prisoner's dilemma games, revealing that the level of hierarchy affects the distribution and prevalence of cooperative behavior.

Contribution

It introduces a hierarchical lattice model for the prisoner's dilemma game and analyzes how hierarchy levels impact cooperation and payoffs through simulations.

Findings

Highest cooperation at top level for Q<4

Middle layers have highest cooperation for larger Q

Four-level hierarchy yields maximum total income

Abstract

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies [D (defector) and C (cooperator)] and their income comes from PD games with the ``neighbors.'' The adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference. Monte Carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels (Q) and by the temptation to defect. According to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low (Q<4). For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average (total) income for the whole community.