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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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    References listed on IDEAS

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    Cited by:

    1. 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; strong equilibrium; Nash equilibrium; Cournot tatonnement;
    All these keywords.

    JEL classification:

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

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