An evolutionary prisoner's dilemma ͑PD͒ game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies ͓D ͑defector͒ and C ͑cooperator͔͒ 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 ͑Q͒ 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 Ͻ 4͒. For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average ͑total͒ income for the whole community.
For example, Vukov and Szabó REF have presented a hierarchical lattice and shown that for different hierarchical levels the highest frequency of cooperators may occur at the top or middle layer.
Evolutionary prisoner’s dilemma game on hierarchical lattices
Physical review. E, Statistical, nonlinear, and soft matter physics
Physical review. E, Statistical, nonlinear, and soft matter physics
Medicine Physics Mathematics