Evolutionary prisoner’s dilemma game on hierarchical lattices

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 $\left(Q\right)$ 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.