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Cournot tatonnement and Nash equilibrium in binary status games

Author

Listed:
  • Nikolai S. Kukushkin

    (Moscow Institute of Physics and Technology, Russia)

  • Pierre von Mouche

    (Wageningen University, The Netherlands)

Abstract

We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property," are established.

Suggested Citation

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-18-00095
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    References listed on IDEAS

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    1. 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.
    2. Thorstein Veblen, 1899. "Mr. Cummings's Strictures on "The Theory of the Leisure Class"," Journal of Political Economy, University of Chicago Press, vol. 8(1), pages 106-106.
    3. 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.
    4. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    5. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    6. 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.
    7. Haagsma, Rein, 2018. "Income inequality and saving in a class society: The role of ordinal status," Economics Discussion Papers 2018-12, Kiel Institute for the World Economy (IfW Kiel).
    8. Nicole Immorlica & Rachel Kranton & Mihai Manea & Greg Stoddard, 2017. "Social Status in Networks," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 1-30, February.
    9. Simon Kuznets, 1942. "Uses of National Income in Peace and War," NBER Chapters, in: Uses of National Income in Peace and War, pages 1-45, National Bureau of Economic Research, Inc.
    10. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    11. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    12. 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.
    13. 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.
    14. Haagsma, Rein, 2018. "Income inequality and saving in a class society: The role of ordinal status," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-31.
    15. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    16. 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.
    17. 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.
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    Cited by:

    1. Kukushkin, Nikolai S., 2019. "Equilibria in ordinal status games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 130-135.
    2. Kukushkin, Nikolai S., 2022. "Ordinal status games on networks," Journal of Mathematical Economics, Elsevier, vol. 100(C).

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    More about this item

    Keywords

    status game; Cournot tatonnement; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D1 - Microeconomics - - Household Behavior

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