Temptation to Defect May Promote Cooperation in Prisoner’s Dilemma Game

Abstract:

In this paper, basing on the prisoner’s dilemma model proposed by M.A.Nowak, we present a model to research the action of temptation to defect in prison’s dilemma model. Firstly, we determine whether a player changes its strategy depends on a Fermi equation which is related to the payoffs of the player and its neighbors. If the player changes its strategy next time step, it will select the strategy adopted by the one who gets the highest payoff among its neighbors as its own strategy. Form the results we find that when four neighbors are considered, the density of cooperators will present a downtrend. Well, when eight neighbors are considered, the density of cooperators will decline at the beginning and increase suddenly afterwards. When twelve neighbors are considered, if the density of cooperators is reduced to zero, cooperation will appear again. Thus, the increase of temptation to defect may promote cooperation.

• Periodical: Applied Mechanics and Materials (Volumes 602-605)
• Pages: 3783-3786
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.602-605.3783
• Online since: August 2014
• Authors: Qiu Hui Pan*, Jia Lin Jia, Kun Jiang, Ming Feng He
• Keywords: Average of Payoffs, Evolution, Fermi Equation, Temptation to Defect

References

[1] C. Darwin , On the Origin of Species by Means of Natural Selection . or the preservation of Favoured Races in the Struggle for Life, 1st Edition, John Murray, London, 1859.

DOI: 10.5962/bhl.title.82303

[2] Nowak M A. Five rules for the evolution of cooperation [J]. Science 314(5805) (2006)1560-1563.

DOI: 10.1126/science.1133755

[3] M.A. Nowak, R.M. May, Evolutionary games and spatial chaos. Nature 359 (1992) 826-829.

DOI: 10.1038/359826a0

[4] Nowak M A, May R M. The spatial dilemmas of evolution [J]. International Journal of Bifurcation and Chaos 3(1) (1993)35-78.

[5] Robert Axelrod, The Evolution of Cooperation, (2006).

[6] G. Szabo, C. Toke, Evolutionary prisoner's dilemma game on a square lattice. Phys. Rev. E (1998) 58, 69.