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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.

Suggested Citation

  • Kukushkin, Nikolai S., 2019. "Equilibria in ordinal status games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 130-135.
  • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:130-135
    DOI: 10.1016/j.jmateco.2019.07.010
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    Cited by:

    1. Kukushkin, Nikolai S., 2020. "Ordinal status games on networks," MPRA Paper 104729, University Library of Munich, Germany.
    2. Le Breton, Michel & Shapoval, Alexander & Weber, Shlomo, 2020. "A Game-Theoretical Model of the Landscape Theory," CEPR Discussion Papers 14993, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Social status; Strong equilibrium; Nash equilibrium; Cournot tatonnement;

    JEL classification:

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

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