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Approximate Nash equilibrium under the single crossing conditions

  • Kukushkin, Nikolai S.

We consider strategic games where strategy sets are linearly ordered while the preferences of the players are described by binary relations. All restrictions imposed on the preferences are satisfied in the case of epsilon-optimization of a bounded-above utility function. A Nash equilibrium exists and can be reached from any strategy profile after a finite number of best response improvements if the single crossing conditions hold w.r.t.\ pairs [one player's strategy, a profile of other players' strategies], and the preference relations are transitive. If, additionally, there are just two players, every best response improvement path reaches a Nash equilibrium after a finite number of steps. If each player is only affected by a linear combination of the strategies of others, the single crossing conditions hold w.r.t.\ pairs [one player's strategy, an aggregate of the strategies of others], and the preference relations are interval orders, then a Nash equilibrium exists and can be reached from any strategy profile with a finite best response path.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 44320.

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Date of creation: 10 Feb 2013
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Handle: RePEc:pra:mprapa:44320
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  1. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. John K.-H. Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Papers 2007-W04, Economics Group, Nuffield College, University of Oxford.
  3. Nikolai S. Kukushkin & Satoru Takahashi & Tetsuo Yamamori, 2005. "Improvement dynamics in games with strategic complementarities," International Journal of Game Theory, Springer, vol. 33(2), pages 229-238, 06.
  4. Nikolai S Kukushkin, 2004. "'Strategic supplements' in games with polylinear interactions," Game Theory and Information 0411008, EconWPA, revised 28 Feb 2005.
  5. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
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  7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  8. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  9. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
  10. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
  11. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, 03.
  12. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  13. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
  14. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.
  15. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
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