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Cyclic dominance in a two-person rock–scissors–paper game

Author

Listed:
  • Liliana Garrido-da-Silva

    (Centro de Matemática da Universidade do Porto (CMUP))

  • Sofia B. S. D. Castro

    (Centro de Matemática da Universidade do Porto (CMUP)
    Centro de Economia e Finanças (Cef.UP))

Abstract

The Rock–scissors–paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players’ payoff when a tie occurs.

Suggested Citation

  • Liliana Garrido-da-Silva & Sofia B. S. D. Castro, 2020. "Cyclic dominance in a two-person rock–scissors–paper game," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 885-912, September.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00706-4
    DOI: 10.1007/s00182-020-00706-4
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/1014 is not listed on IDEAS
    2. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    3. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
    4. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    5. Michael D. Noel, 2007. "Edgeworth Price Cycles: Evidence From The Toronto Retail Gasoline Market," Journal of Industrial Economics, Wiley Blackwell, vol. 55(1), pages 69-92, March.
    6. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    7. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Price setting; Rock–scissors–paper game; Cyclic dynamics; Stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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