Equilibria in ordinal status games

Nikolai Kukushkin ()

MPRA Paper from University Library of Munich, Germany

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.

Keywords: status game; strong equilibrium; Nash equilibrium; Cournot tatonnement (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018-06-28
New Economics Papers: this item is included in nep-gth, nep-hpe, nep-mic and nep-upt
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Journal Article: Equilibria in ordinal status games (2019)
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