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Characterizing Von Neumann-Morgenstern Stable Sets in Infinite Sets

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  • Athanasios Andrikopoulos
  • Nikolaos Sampanis

Abstract

The theory of optimal choice sets provides a well-established framework in social choice and game theory. When preferences are cyclic, as often occurs in complex economic environments, the set of maximal elements may be empty, thereby motivating alternative solution concepts such as the von Neumann--Morgenstern (vNM) stable set. In this paper, we study binary relations on infinite sets of alternatives within an order-theoretic and topological framework. Our main result yields a topological characterization of von Neumann--Morgenstern stable maximality: for consistent abstract decision problems satisfying Upper MacNeille Informational Monotonicity, the set of maximal elements is non-empty and stable if and only if there exists a compact topology on \(X\) with respect to which \(R\) is Nachbin closed and upper semicontinuous.

Suggested Citation

  • Athanasios Andrikopoulos & Nikolaos Sampanis, 2026. "Characterizing Von Neumann-Morgenstern Stable Sets in Infinite Sets," Papers 2607.26559, arXiv.org.
    • Handle: RePEc:arx:papers:2607.26559
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    References listed on IDEAS

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    1. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    2. Athanasios Andrikopoulos, 2023. "A topological characterization of generalized stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 1-9, July.
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