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Self-organization in a simple model of adaptive agents playing 2×2 games with arbitrary payoff matrices

H. Fort1 and S. Viola2

  • 1Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
  • 2Instituto de Física, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay

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Phys. Rev. E 69, 036110 – Published 23 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.036110

Abstract

We analyze, both analytically and numerically, the self-organization of a system of “selfish” adaptive agents playing an arbitrary iterated pairwise game (defined by a 2×2 payoff matrix). Examples of possible games to play are the prisoner’s dilemma (PD) game, the chicken game, the hero game, etc. The agents have no memory, use strategies not based on direct reciprocity nor “tags” and are chosen at random, i.e., geographical vicinity is neglected. They can play two possible strategies: cooperate (C) or defect (D). The players measure their success by comparing their utilities with an estimate for the expected benefits and update their strategy following a simple rule. Two versions of the model are studied: (1) the deterministic version (the agents are either in definite states C or D) and (2) the stochastic version (the agents have a probability c of playing C). Using a general master equation we compute the equilibrium states into which the system self-organizes, characterized by their average probability of cooperation ceq. Depending on the payoff matrix, we show that ceq can take five different values. We also consider the mixing of agents using two different payoff matrices and show that any value of ceq can be reached by tuning the proportions of agents using each payoff matrix. In particular, this can be used as a way to simulate the effect of a fraction d of “antisocial” individuals—incapable of realizing any value to cooperation—on the cooperative regime hold by a population of neutral or “normal” agents.

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Outline

Information

Phys. Rev. E 69, 036110– Published 23 March, 2004
  • Received 3 October 2003

© 2004 American Physical Society

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