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Mean-field approximation for two- and three-person Prisoner’s Dilemmas

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  • Platkowski, Tadeusz
  • Siwak, Michal

Abstract

We consider the mean-field approximation (MFA) to the system of interacting agents playing two- and three-person Prisoner’s Dilemma games (2-PD and 3-PD). The agents have three available strategies: All-C, All-D, and a third one, which we choose in various ways. Long-time distribution of the strategies is compared for both games. The latter game admits coexistence of larger number of strategies in the long run. In the case of external pressure for cooperation, more pressure is in general necessary for 3-PD than for 2-PD to guarantee cooperation for almost all initial compositions of the strategies. Results for different types of tit-for-tat strategies for 3-PD are discussed. Unlike the 2-PD case, the more forgiving tit-for-tat strategy can survive in the long run in 3-PD.

Suggested Citation

  • Platkowski, Tadeusz & Siwak, Michal, 2008. "Mean-field approximation for two- and three-person Prisoner’s Dilemmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2909-2918.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:12:p:2909-2918
    DOI: 10.1016/j.physa.2008.01.098
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    1. J R Hoffmann, "undated". "The Evolution of Cooperation Revisited," SMF Discussion Paper Series 9606, University of Nottingham, School of Management & Finance.
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