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

  • Eric Bahel
  • Hans Haller

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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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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  1. Eric Bahel, 2011. "Rock-Paper-Scissors and Cycle-Based Games," Working Papers e07-31, Virginia Polytechnic Institute and State University, Department of Economics.
  2. 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.
  3. 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.
  4. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
  5. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
  6. A. van den Nouweland, 2007. "Rock-Paper-Scissors; A New and Elegant Proof," Department of Economics - Working Papers Series 1003, The University of Melbourne.
  7. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
  8. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
  9. Yves Sprumont, 2005. "On the Discrete Version of the Aumann-Shapley Cost-Sharing Method," Econometrica, Econometric Society, vol. 73(5), pages 1693-1712, 09.
  10. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer, vol. 56(2), pages 219-249, June.
  11. repec:ebl:ecbull:v:3:y:2007:i:43:p:1-6 is not listed on IDEAS
  12. 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.
  13. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 2004-14, Universite de Montreal, Departement de sciences economiques.
  14. 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.
  15. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, vol. 41(3), pages 553-564, August.
  16. 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.
  17. Anne van den Nouweland, 2007. "Rock-paper-scissors a new and elegant proof," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-6.
  18. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
  19. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
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