Equilibrium non-existence in generalized games

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Abstract

A generalized game is a strategic situation in which agents' behavior restricts their opponents' available action choices, giving rise to interdependencies in terms of what strategy profiles remain mutually feasible. This paper proposes a novel example of a simple jointly convex generalized game in which the well-known convexity, compactness, continuity, and concavity assumptions are satisfied, but no Nash equilibrium exists. The essence of this contribution lies in answering a question left open by Banks and Duggan (2004): whether the supplemental condition of lower hemicontinuity of feasibility correspondences can be dropped from these authors' equilibrium-existence theorem. It cannot.

Original languageEnglish (US)
Pages (from-to)327-337
Number of pages11
JournalGames and Economic Behavior
Volume135
DOIs
StatePublished - Sep 2022

Keywords

  • Existence
  • Generalized games
  • Nash equilibrium

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

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