Evolutionary prisoner’s dilemma games with local interaction and best-response dynamics

Abstract

This paper studies the long run behavior in evolutionary prisoner’s dilemma games. All players are assumed to sit around a circle and to interact only with their neighbors. It is known that full-defection is the unique long run equilibrium as the probability of players’ experimentation (or mutation) tends to zero in the best response dynamics. Here, it is shown that full-cooperation could emerge in the long run if one also cares for his neighbors in the bestresponse dynamics.

Keywords

Prisoner’s dilemma game / full cooperation / best response / local interaction / long run equilibrium / parallel updating

References

[1] Bergstrom T C, Stark O. How altruism can prevail in an evolutionary environment. Amer Econ Rev, 1993, 83: 149-155

[2] Chen H C, Chow Y. Evolutionary prisoner’s dilemma games with one-dimensional local interaction and imitation. Adv Appl Probab, 2009, 41: 154-176

[3] Chiang T S, Chow Y. A limit theorem for a class of inhomogeneous Markov processes. Ann Probab, 1989, 17: 1483-1502

[4] Ellison G. Learning, local interaction, and coordination. Econometrica, 1993, 61: 1047-1071

[5] Eshel I, Samuelson L, Shaked A. Altruists, egoists, and hooligans in a local interaction model. Amer Econ Rev, 1998, 88: 157-179

[6] Freidlin M I, Wentzell A D. Random Perturbations of Dynamical Systems. New York: Springer-Verlag, 1984

[7] Kandori M G, Mailath G, Rob R. Learning, mutation, and long-run equilibria in games. Econometrica, 1993, 61: 29-56

[8] Karandikar R D, Mookherjee D R, Vega-Redondo F. Evolving aspirations and cooperation. J Econom Theory, 1998, 80: 292-332

[9] Nowak M A, Sigmund K. Invasion dynamics of the finitely repeated prisoner’s dilemma. Games Econom Behav, 1995, 11: 364-390

[10] Palomino F, Vega-Redondo F. Convergence of aspirations and partial cooperation in the prisoner’s dilemma. Int J Game Theory, 1999, 28: 465-488

[11] Robson A J, Vega-Redondo F. Efficient equilibrium selection in evolutionary games with random matching. J Econom Theory, 1996, 70: 65-92

[12] Vega-Redondo F. Economics and the Theory of Games. Cambridge: Cambridge University Press, 2003

[13] Wang J. The Theory of Games. Beijing: Tsinghua University Press, 1988

[14] Wiseman T, Yilankaya O. Cooperation, secret handshakes, and imitation in the prisoner’s dilemma. Games Econom Behav, 2001, 37: 216-242

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