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Better response dynamics and Nash equilibrium in discontinuous games

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  • Kukushkin, Nikolai S.

Abstract

Philip Reny’s approach to games with discontinuous utility functions can work outside its original context. The existence of Nash equilibrium and the possibility to approach the equilibrium set with a finite number of individual improvements are established, under conditions weaker than the better reply security, for three classes of strategic games: potential games, games with strategic complements, and aggregative games with appropriate monotonicity conditions.

Suggested Citation

  • Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:68-78
    DOI: 10.1016/j.jmateco.2017.11.005
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    1. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    2. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    3. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," PSE-Ecole d'économie de Paris (Postprint) hal-00750953, HAL.
    4. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Post-Print halshs-00426402, HAL.
    5. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    6. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    7. Martin Kaae Jensen, 2018. "Aggregative games," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 4, pages 66-92, Edward Elgar Publishing.
    8. 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.
    9. Nikolai S. Kukushkin, 2016. "Cournot Tatonnement in Aggregative Games with Monotone Best Responses," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 31-45, Springer.
    10. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    11. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
    12. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    13. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
    14. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    15. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    16. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Post-Print hal-00750953, HAL.
    17. Prokopovych, Pavlo & Yannelis, Nicholas C., 2017. "On strategic complementarities in discontinuous games with totally ordered strategies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 147-153.
    18. Nikolai Kukushkin, 2013. "Monotone comparative statics: changes in preferences versus changes in the feasible set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1039-1060, April.
    19. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Documents de travail du Centre d'Economie de la Sorbonne 09061, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    20. Wakker, Peter, 1988. "Continuity of Preference Relations for Separable Topologies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 105-110, February.
    21. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    22. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00750953, HAL.
    23. Nikolai S Kukushkin, 2004. "'Strategic supplements' in games with polylinear interactions," Game Theory and Information 0411008, University Library of Munich, Germany, revised 28 Feb 2005.
    24. Philippe Bich, 2009. "Existence of pure Nash equilibria in discontinuous and non quasiconcave games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426402, HAL.
    25. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 17-29, September.
    26. Nikolai Kukushkin, 2011. "Nash equilibrium in compact-continuous games with a potential," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 387-392, May.
    27. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    28. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    29. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
    30. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    31. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
    32. Nikolai S. Kukushkin & Satoru Takahashi & Tetsuo Yamamori, 2005. "Improvement dynamics in games with strategic complementarities," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 229-238, June.
    33. Pavlo Prokopovych, 2013. "The single deviation property in games with discontinuous payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 383-402, June.
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    Cited by:

    1. Ben Amiet & Andrea Collevecchio & Kais Hamza, 2020. "When "Better" is better than "Best"," Papers 2011.00239, arXiv.org.
    2. Kukushkin, Nikolai S., 2022. "Ordinal status games on networks," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    3. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    4. Guanghui Yang & Chanchan Li & Jinxiu Pi & Chun Wang & Wenjun Wu & Hui Yang, 2021. "Characterizations of Pareto-Nash Equilibria for Multiobjective Potential Population Games," Mathematics, MDPI, vol. 9(1), pages 1-13, January.
    5. Kukushkin, Nikolai S., 2019. "Equilibria in ordinal status games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 130-135.
    6. Nikolai S. Kukushkin & Pierre von Mouche, 2018. "Cournot tatonnement and Nash equilibrium in binary status games," Economics Bulletin, AccessEcon, vol. 38(2), pages 1038-1044.
    7. zhao, guo & Chai, Yingming, 2024. "A Sufficient Condition for Weakly Acyclic games with Applications," MPRA Paper 120789, University Library of Munich, Germany.

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    More about this item

    Keywords

    Discontinuous game; Potential game; Bertrand competition; Strategic complements; Aggregative game;
    All these keywords.

    JEL classification:

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

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