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Equilibrium non-existence in generalized games

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  • Tóbiás, Áron

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.

Suggested Citation

  • Tóbiás, Áron, 2022. "Equilibrium non-existence in generalized games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 327-337.
    • Handle: RePEc:eee:gamebe:v:135:y:2022:i:c:p:327-337
    DOI: 10.1016/j.geb.2022.06.012
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    References listed on IDEAS

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    1. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    2. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    3. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
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    More about this item

    Keywords

    Generalized games; Nash equilibrium; Existence;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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