Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise

Conflict of interest may be modeled, heuristically, by the iterated Prisoner's Dilemma game. Although several researchers have shown that the Tit-For-Tat strategy can encourage the evolution of cooperation, this strategy can never outscore any opponent and it does poorly against its clone in a noisy environment. Here we examine the family of Pavlovian strategies which adapts its play by positive and negative conditioning, much as many animals do. Mutual cooperation will evolve in a contest with Pavlov against a wide variety of opponents and in particular against its clone. And the strategy is quite stable in a noisy environment. Although this strategy cooperates and retaliates, as does Tit-For-Tat, it is not forgiving; Pavlov will exploit altruistic strategies until he is punished by mutual defection. Moreover, Pavlovian strategies are natural models for many real life conflict-of-interest encounters as well as human and computer simulations.

[1]  M. Shubik Game theory, behavior, and the paradox of the Prisoner's Dilemma: three solutions , 1970 .

[2]  Christian Donninger,et al.  Is it Always Efficient to be Nice? A Computer Simulation of Axelrod’s Computer Tournament , 1986 .

[3]  Michael W. Macy,et al.  Walking out of Social Traps , 1989 .

[4]  S. Komorita,et al.  Reciprocity and Cooperation in Social Dilemmas , 1991 .

[5]  M. Lombardo,et al.  Mutual Restraint in Tree Swallows: A Test of the TIT FOR TAT Model of Reciprocity , 1985, Science.

[6]  Michael Orkin Balanced Strategies for Prisoner's Dilemma , 1987 .

[7]  Martin A. Nowak,et al.  Game-dynamical aspects of the prisoner's dilemma , 1989 .

[8]  M. Macy Learning to Cooperate: Stochastic and Tacit Collusion in Social Exchange , 1991, American Journal of Sociology.

[9]  M. Nowak,et al.  The evolution of stochastic strategies in the Prisoner's Dilemma , 1990 .

[10]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[11]  Ulrich Mueller,et al.  Optimal Retaliation for Optimal Cooperation , 1987 .

[12]  Underwood Dudley Elementary Number Theory , 1978 .

[13]  R. May More evolution of cooperation , 1987, Nature.

[14]  R. Axelrod,et al.  The Further Evolution of Cooperation , 1988, Science.

[15]  D. Kraines,et al.  Pavlov and the prisoner's dilemma , 1989 .

[16]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[17]  M. Patchen,et al.  Strategies for Eliciting Cooperation from an Adversary , 1987 .

[18]  George J. Mailath,et al.  Introduction: Symposium on evolutionary game theory , 1992 .

[19]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[20]  Roderick M. Kramer,et al.  When in Doubt... , 1991 .

[21]  P. Molander The Optimal Level of Generosity in a Selfish, Uncertain Environment , 1985 .

[22]  A. Rapoport,et al.  Prisoner's Dilemma , 1965 .

[23]  R. Axelrod Annotated bibliography on The Evolution of Cooperation , 1994 .

[24]  V. Edwin Bixenstine,et al.  Strategies of "real" opponents in eliciting cooperative choice in a Prisoner's Dilemma game , 1971 .

[25]  H. Simon,et al.  A mechanism for social selection and successful altruism. , 1990, Science.