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Cycles with undistinguished actions and extended Rock–Paper–Scissors games

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  • Bahel, Eric
  • Haller, Hans

Abstract

This paper examines zero-sum games that are based on a cyclic preference relation defined over undistinguished 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. Our results give some insights as to the robustness of Nash equilibria with respect to perturbations of the action set.

Suggested Citation

  • Bahel, Eric & Haller, Hans, 2013. "Cycles with undistinguished actions and extended Rock–Paper–Scissors games," Economics Letters, Elsevier, vol. 120(3), pages 588-591.
    • Handle: RePEc:eee:ecolet:v:120:y:2013:i:3:p:588-591
    DOI: 10.1016/j.econlet.2013.06.018
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    References listed on IDEAS

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    1. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    2. Harborne W. Stuart Jr. & Hong Hu, 2002. "An epistemic analysis of the Harsanyi transformation," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 517-525.
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    4. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    5. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    6. Bahel, Eric, 2012. "Rock–paper–scissors and cycle-based games," Economics Letters, Elsevier, vol. 115(3), pages 401-403.
    7. Anne van den Nouweland, 2007. "Rock-paper-scissors a new and elegant proof," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-6.
    8. A. van den Nouweland, 2007. "Rock-Paper-Scissors; A New and Elegant Proof," Department of Economics - Working Papers Series 1003, The University of Melbourne.
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    Cited by:

    1. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    2. Bahel, Eric, 2021. "Patent Nash equilibria in symmetric strictly competitive games," Economics Letters, Elsevier, vol. 199(C).

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    More about this item

    Keywords

    Cycle; Nash equilibrium; Minimax theorem;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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