title: Phase diagrams for three-strategy evolutionary prisoner's dilemma games on regular graphs.
abstract: Evolutionary prisoner's dilemma games are studied with players located on square lattice and random regular graph defining four neighbors for each one. The players follow one of the three strategies: tit-for-tat, unconditional cooperation, and defection. The simplified payoff matrix is characterized by two parameters: the temptation b to choose defection and the cost c of inspection reducing the income of tit-for-tat. The strategy imitation from one of the neighbors is controlled by pairwise comparison at a fixed level of noise. Using Monte Carlo simulations and the extended versions of pair approximation we have evaluated the b-c phase diagrams indicating a rich plethora of phase transitions between stationary coexistence, absorbing, and oscillatory states, including continuous and discontinuous phase transitions. By reasonable costs the tit-for-tat strategy prevents extinction of cooperators across the whole span of b determining the prisoner's dilemma game, irrespective of the connectivity structure. We also demonstrate that the system can exhibit a repetitive succession of oscillatory and stationary states upon changing a single payoff value, which highlights the remarkable sensitivity of cyclical interactions on the parameters that define the strength of dominance.
authors.affiliation: Research Institute for Technical Physics and Materials Science, Budapest, Hungary.
authors.forename: Attila
authors.initials: A
authors.lastname: Szolnoki
authors.forename: Matjaz
authors.initials: M
authors.lastname: Perc
authors.forename: György
authors.initials: G
authors.lastname: Szabó
mesh_terms: D005075:Biological Evolution; D001703:Biophysics / Q000379:methods; D003198:Computer Simulation; D004926:Escherichia coli / Q000235:genetics* / Q000502:physiology; D005716:Game Theory; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009991:Oscillometry / Q000379:methods