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Pure Saddle Points and Symmetric Relative Payoff Games

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  • Duersch, Peter
  • Oechssler, Joerg
  • Schipper, Burkhard C

Abstract

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20864.

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Date of creation: 21 Feb 2010
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Handle: RePEc:pra:mprapa:20864

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Keywords: symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability;

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  1. Tobias Guse & Burkhard Hehenkamp & Alex Possajennikov, 2008. "On the Equivalence of Nash and Evolutionary Equilibrium in Finite Populations," Discussion Papers, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham 2008-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  2. Burkhard Hehenkamp & Wolfgang Leininger & Alex Possajennikov, 2003. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation," Discussion Papers in Economics 03_01, University of Dortmund, Department of Economics.
  3. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-48, March.
  4. Duffy, John & Matros, Alexander & Temzelides, Ted, 2011. "Competitive behavior in market games: Evidence and theory," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1437-1463, July.
  5. Walker, James M. & Gardner, Roy & Ostrom, Elinor, 1990. "Rent dissipation in a limited-access common-pool resource: Experimental evidence," Journal of Environmental Economics and Management, Elsevier, vol. 19(3), pages 203-211, November.
  6. Alex Possajennikov, 2003. "Evolutionary foundations of aggregate-taking behavior," Economic Theory, Springer, vol. 21(4), pages 921-928, 06.
  7. Radzik, Tadeusz, 1991. "Saddle Point Theorems," International Journal of Game Theory, Springer, vol. 20(1), pages 23-32.
  8. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
  9. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2011. "Unbeatable Imitation," Working Papers 103, University of California, Davis, Department of Economics.
  10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  11. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
  12. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  13. Tanaka, Yasuhito, 2000. "A finite population ESS and a long run equilibrium in an n players coordination game," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 195-206, March.
  14. Wolfgang Leininger, 2006. "Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games," Economic Theory, Springer, vol. 29(3), pages 713-719, November.
  15. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, Econometric Society, vol. 65(2), pages 375-384, March.
  16. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  17. Branzei, Rodica & Mallozzi, Lina & Tijs, Stef, 2003. "Supermodular games and potential games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 39-49, February.
  18. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
  19. Brânzei, R. & Mallozzi, L. & Tijs, S.H., 2003. "Supermodular games and potential games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121822, Tilburg University.
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Cited by:
  1. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Unbeatable Imitation," MPRA Paper 20856, University Library of Munich, Germany.

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