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Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors

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  • William C. Grant

    (Department of Economics, James Madison University, Harrisonburg, VA 22807, USA)

Abstract

In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.

Suggested Citation

  • William C. Grant, 2023. "Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors," Games, MDPI, vol. 14(3), pages 1-16, May.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:3:p:45-:d:1159260
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    References listed on IDEAS

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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    4. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 551-556.
    5. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. Lars P. Metzger, 2018. "Evolution and correlated equilibrium," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 333-346, April.
    8. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
    9. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
    10. Kristof Bosmans & Z. Emel Öztürk, 2018. "An axiomatic approach to the measurement of envy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 247-264, February.
    11. Lenzo, Justin & Sarver, Todd, 2006. "Correlated equilibrium in evolutionary models with subpopulations," Games and Economic Behavior, Elsevier, vol. 56(2), pages 271-284, August.
    12. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
    13. Elvio Accinelli & Filipe Martins & Jorge Oviedo, 2019. "Evolutionary Game Theory: A Generalization of the ESS Definition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, December.
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