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Equilibria in ordinal status games

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  • Kukushkin, Nikolai S.

Abstract

Several agents choose positions on the real line (e.g., their levels of conspicuous consumption). Each agent's utility depends on her choice and her "status," which, in turn, is determined by the number of agents with greater choices (the fewer, the better). If the rules for the determination of the status are such that the set of the players is partitioned into just two tiers ("top" and "bottom"), then a strong Nash equilibrium exists, which Pareto dominates every other Nash equilibrium. Moreover, the Cournot tatonnement process started anywhere in the set of strategy profiles inevitably reaches a Nash equilibrium in a finite number of steps. If there are three tiers ("top," "middle," and "bottom"), then the existence of a Nash equilibrium is ensured under an additional assumption; however, there may be no Pareto efficient equilibrium. With more than three possible status levels, there seems to be no reasonably general sufficient conditions for Nash equilibrium existence.

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  • Kukushkin, Nikolai S., 2018. "Equilibria in ordinal status games," MPRA Paper 87635, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:87635
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    1. Thorstein Veblen, 1899. "Mr. Cummings's Strictures on "The Theory of the Leisure Class"," Journal of Political Economy, University of Chicago Press, vol. 8, pages 106-106.
    2. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    3. Frank, Robert H, 1985. "The Demand for Unobservable and Other Nonpositional Goods," American Economic Review, American Economic Association, vol. 75(1), pages 101-116, March.
    4. 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.
    5. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    6. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
    7. KennethJ. Arrow & ParthaS. Dasgupta, 2009. "Conspicuous Consumption, Inconspicuous Leisure," Economic Journal, Royal Economic Society, vol. 119(541), pages 497-516, November.
    8. Bilancini, Ennio & Boncinelli, Leonardo, 2008. "Ordinal vs cardinal status: Two examples," Economics Letters, Elsevier, vol. 101(1), pages 17-19, October.
    9. 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.
    10. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    11. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    12. Veblen, Thorstein, 1899. "The Theory of the Leisure Class," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number veblen1899.
    13. 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.
    14. 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.
    15. Haagsma Rein & van Mouche Pierre, 2010. "Equilibrium Social Hierarchies: A Non-Cooperative Ordinal Status Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-49, June.
    16. Gary S. Becker & Kevin M. Murphy & Ivan Werning, 2005. "The Equilibrium Distribution of Income and the Market for Status," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 282-310, April.
    17. Clark, Andrew E. & Oswald, Andrew J., 1998. "Comparison-concave utility and following behaviour in social and economic settings," Journal of Public Economics, Elsevier, vol. 70(1), pages 133-155, October.
    18. Rauscher, Michael, 1992. "Keeping up with the Joneses : Chaotic patterns in a status game," Economics Letters, Elsevier, vol. 40(3), pages 287-290, November.
    19. 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:

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    More about this item

    Keywords

    status game; strong equilibrium; Nash equilibrium; Cournot tatonnement;

    JEL classification:

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

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