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Von Neumann–Morgenstern Hypergraphs

Author

Listed:
  • Stefano Vannucci

    (Department of Economics and Statistics, University of Siena, Piazza San Francesco 7, 53100 Siena, Italy)

Abstract

A simple hypergraph H with vertex set X and edge set E is representable by Von Neumann–Morgenstern (VNM)-stable sets—or VNM—if there exists an irreflexive simple digraph D with vertex set X such that each edge of H is a VNM-stable set of D . It is shown that a simple hypergraph H is VNM if and only if each edge of H is a maximal clique of the conjugation graph of H . A related algorithm that identifies finite VNM hypergraphs is also provided.

Suggested Citation

  • Stefano Vannucci, 2025. "Von Neumann–Morgenstern Hypergraphs," Games, MDPI, vol. 16(2), pages 1-6, April.
    • Handle: RePEc:gam:jgames:v:16:y:2025:i:2:p:17-:d:1634872
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    References listed on IDEAS

    as
    1. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590, Elsevier.
    2. Wilson, Robert B., 1970. "The finer structure of revealed preference," Journal of Economic Theory, Elsevier, vol. 2(4), pages 348-353, December.
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