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Cycles with Undistinguished Actions and Extended Rock-Paper-Scissors Games

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  • Eric Bahel
  • Hans Haller
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    Abstract

    The present paper examines zero-sum games that are based on a cyclic preference relation defined over anonymous actions. For each of these games, the set of Nash equilibria is characterized. When the number of actions is odd, a unique Nash equilibrium is always obtained. On the other hand, in the case of an even number of actions, every such game exhibits an infinite number of Nash equilibria. As a special case, a proof of the uniqueness of the Nash equilibrium for the Rock-Paper-Scissors game obtains.

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    File URL: ftp://repec.econ.vt.edu/Papers/Bahel/GRPS-6.pdf
    File Function: First version, 2012
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    Bibliographic Info

    Paper provided by Virginia Polytechnic Institute and State University, Department of Economics in its series Working Papers with number e07-35.

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    Length: 48 pages
    Date of creation: 2012
    Date of revision:
    Handle: RePEc:vpi:wpaper:e07-35

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    Keywords: cycle; Nash equilibrium; minimax theorem.;

    This paper has been announced in the following NEP Reports:

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    1. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
    2. Angeles de Frutos, M., 1998. "Decreasing Serial Cost Sharing under Economies of Scale," Journal of Economic Theory, Elsevier, vol. 79(2), pages 245-275, April.
    3. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer, vol. 37(2), pages 155-184, June.
    4. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer, vol. 40(3), pages 551-589, August.
    5. Nouweland, C.G.A.M.. van den & Potters, J. & Tijs, S.H. & Zarzuelo, J., 1991. "Cores and related solution concepts for multi-choice games," Research Memorandum 478, Tilburg University, Faculty of Economics and Business Administration.
    6. Yair Tauman & Naoki Watanabe, 2007. "The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results," Economic Theory, Springer, vol. 30(1), pages 135-149, January.
    7. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer, vol. 42(2), pages 439-460, May.
    8. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
    9. MOULIN, Hervé & SPRUMONT, Yves, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 28-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Yves Sprumont, 2005. "On the Discrete Version of the Aumann-Shapley Cost-Sharing Method," Econometrica, Econometric Society, vol. 73(5), pages 1693-1712, 09.
    11. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    12. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
    13. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
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