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Iterated symmetric three-player prisoner’s dilemma game

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  • El-Seidy, Essam
  • Soliman, Karim.M.

Abstract

Although, most game theory researches on the prisoner’s dilemma have centered on two-player models, it is possible to create it to be consisted of three or even more players. In this paper, we are interested in the model of three-player iterated prisoner’s dilemma game where, each player has two choices. The action of each strategy in this model depends on the previous action of the last round. Each strategy is presented by finite state of automata. We used a computer program to calculate the payoff values resulting from the actions of all possible strategies. We study the behavior of four different strategies related to Tit for Tat concept. The conditions of each strategy to be the best are determined. In Appendix section, we design an algorithm and implement it using the Java programing language to facilitate the calculations.

Suggested Citation

  • El-Seidy, Essam & Soliman, Karim.M., 2016. "Iterated symmetric three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 117-127.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:117-127
    DOI: 10.1016/j.amc.2016.02.009
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    1. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    2. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    3. Hammerstein, Peter & Selten, Reinhard, 1994. "Game theory and evolutionary biology," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 28, pages 929-993, Elsevier.
    4. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    5. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
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    1. EL-Seidy, Essam & Elshobaky, Entisarat.M. & Soliman, Karim.M., 2016. "Two population three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 44-53.
    2. El-Salam, Salsabeel M. Abd & El-Seidy, Essam & Abdel-Malek, Amira R., 2023. "Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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