IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v16y2025i2p17-d1634872.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/16/2/17/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/16/2/17/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jung, Hanjoon Michael, 2009. "Spatial pillage game," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 701-707, December.
    2. Thomas Demuynck & P. Jean‐Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "The Myopic Stable Set for Social Environments," Econometrica, Econometric Society, vol. 87(1), pages 111-138, January.
    3. Nunnari, Salvatore, 2021. "Dynamic legislative bargaining with veto power: Theory and experiments," Games and Economic Behavior, Elsevier, vol. 126(C), pages 186-230.
    4. Atay, Ata & Núñez, Marina, 2019. "A note on the relationship between the core and stable sets in three-sided markets," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 10-14.
    5. Jinpeng Ma, 1998. "Strategic Formation of Coalitions," Departmental Working Papers 199810, Rutgers University, Department of Economics.
    6. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. , & , J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
    8. Anesi, Vincent & Seidmann, Daniel J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
    9. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    10. Dylan Laplace Mermoud, 2023. "Geometry of Set Functions in Game Theory: Combinatorial and Computational Aspects," Papers 2301.02950, arXiv.org, revised Oct 2023.
    11. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
    12. Rowat, Colin & Kerber, Manfred, 2014. "Sufficient conditions for unique stable sets in three agent pillage games," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 69-80.
    13. Francesc Llerena & Carlos Rafels Pallarola, 2004. "Max-convex decompositions for cooperative TU games," Working Papers in Economics 123, Universitat de Barcelona. Espai de Recerca en Economia.
    14. Francesc Llerena & Carles Rafels, 2013. "Stable sets and max-convex decompositions of TU games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 313-322, July.
    15. J. Jordan, 2009. "Power and efficiency in production pillage games," Review of Economic Design, Springer;Society for Economic Design, vol. 13(3), pages 171-193, September.
    16. Bhaskar Dutta & Hannu Vartiainen, 2018. "Coalition Formation and History Dependence," Working Papers 1006, Ashoka University, Department of Economics.
    17. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    18. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    19. Weibin Han & Adrian Deemen & D. Ary A. Samsura, 2016. "A note on extended stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 265-275, August.
    20. Demuynck, Thomas & Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Myopic Stable Set for Social Environments (RM/17/002-revised)," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:16:y:2025:i:2:p:17-:d:1634872. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.