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Cournot tatonnement and Nash equilibrium in binary status games

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  • Kukushkin, Nikolai S.
  • von Mouche, Pierre H.M.

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

  • Kukushkin, Nikolai S. & von Mouche, Pierre H.M., 2018. "Cournot tatonnement and Nash equilibrium in binary status games," MPRA Paper 86178, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:86178
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    References listed on IDEAS

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    10. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
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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:

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

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