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The Geometry of Solution Concepts for N-Person Cooperative Games

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  • Richard Spinetto

    (University of Colorado)

Abstract

The closed convex polyhedron consisting of all 0-1 normal n-person games with nonempty core is characterized by naming its extreme points. This characterization establishes a geometric setting, in the game space itself, for such solution concepts as the core and the nucleolus. This geometric setting also suggests new solution concepts. A similar geometric setting is also established for the Shapley value, and core and nucleolus solution concepts can be defined in this geometric setting.

Suggested Citation

  • Richard Spinetto, 1974. "The Geometry of Solution Concepts for N-Person Cooperative Games," Management Science, INFORMS, vol. 20(9), pages 1292-1299, May.
    • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:9:p:1292-1299
    DOI: 10.1287/mnsc.20.9.1292
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    Cited by:

    1. Jean Derks & Hans Peters & Peter Sudhölter, 2014. "On extensions of the core and the anticore of transferable utility games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 37-63, February.
    2. Tiziana Ciano & Massimiliano Ferrara & Mariangela Gangemi & Domenica Stefania Merenda & Bruno Antonio Pansera, 2021. "Climate Change Sustainability: From Bargaining to Cooperative Balanced Approach," Games, MDPI, vol. 12(2), pages 1-13, May.
    3. Chen, Haoxun, 2017. "Undominated nonnegative excesses and core extensions of transferable utility games," European Journal of Operational Research, Elsevier, vol. 261(1), pages 222-233.
    4. H. Andrew Michener & Greg B. Macheel & Charles G. Depies & Chris A. Bowen, 1986. "Mollifier Representation in Non-Constant-Sum Games," Journal of Conflict Resolution, Peace Science Society (International), vol. 30(2), pages 361-382, June.

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