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A characterization of vNM-stable sets for linear production games

Author

Listed:
  • Joachim RosenmØller

    (Institut fØr Mathematische Wirtschaftsforschung, UniversitÄt Bielefeld, D-33615 Bielefeld, Germany Department of Economics, Haifa University, Mount Carmel, Haifa 31905, Israel)

  • Benyamin Shitovitz

    (Institut fØr Mathematische Wirtschaftsforschung, UniversitÄt Bielefeld, D-33615 Bielefeld, Germany Department of Economics, Haifa University, Mount Carmel, Haifa 31905, Israel)

Abstract

We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures. Within this context we consider vNM-Stable Sets according to von Neumann and Morgenstern. We classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many imputations. Specifically, in each convex polyhedral vNM-Stable Set (and not only in the symmetric ones), the different types of traders must organize themselves into cartels. The vNM-Stable Set is then the convex hull of the utility distributions of the cartels. Using the results from the continuum, we obtain a similar characterization also for finite glove market games.

Suggested Citation

  • Joachim RosenmØller & Benyamin Shitovitz, 2000. "A characterization of vNM-stable sets for linear production games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 39-61.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:39-61
    Note: Received December 1998/Revised version June 1999
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    Citations

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    Cited by:

    1. Rosenmüller, Joachim, 2014. "Convex vNM–Stable Sets for a Semi Orthogonal Game. Part I: epsilon–Relevant Coalitions," Center for Mathematical Economics Working Papers 483, Center for Mathematical Economics, Bielefeld University.
    2. Núñez, Marina & Vidal-Puga, Juan, 2022. "Stable cores in information graph games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 353-367.
    3. Joachim Rosenmüller & Benyamin Shitovitz, 2010. "Convex vNM-stable sets for linear production games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 311-318, July.
    4. Rosenmüller, Joachim, 2015. "Convex vNM-Stable Sets for a Semi Orthogonal Game. Part IV: Large Economies: the Existence Theorem," Center for Mathematical Economics Working Papers 534, Center for Mathematical Economics, Bielefeld University.
    5. Rosenmüller, Joachim, 2017. "The endogenous formation of cartels," Center for Mathematical Economics Working Papers 318, Center for Mathematical Economics, Bielefeld University.

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