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Preconvex games

Author

Listed:
  • Eric Bahel

    (Department of Economics, Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    (Department of Economics, University of Windsor)

  • Haoyu Wang

    (Department of Economics, Virginia Polytechnic Institute and State University)

Abstract

We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent's marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.

Suggested Citation

  • Eric Bahel & Christian Trudeau & Haoyu Wang, 2025. "Preconvex games," Working Papers 2501, University of Windsor, Department of Economics.
    • Handle: RePEc:wis:wpaper:2501
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    File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/2501.pdf
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    References listed on IDEAS

    as
    1. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    2. Marina Núñez & Carles Rafels, 1998. "On extreme points of the core and reduced games," Annals of Operations Research, Springer, vol. 84(0), pages 121-133, December.
    3. Atay, Ata & Trudeau, Christian, 2024. "Queueing games with an endogenous number of machines," Games and Economic Behavior, Elsevier, vol. 144(C), pages 104-125.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    6. Mackenzie, Andrew & Trudeau, Christian, 2023. "On Groves mechanisms for costly inclusion," Theoretical Economics, Econometric Society, vol. 18(3), July.
    7. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    8. Skoda, Alexandre & Venel, Xavier, 2023. "Weighted average-convexity and Shapley values," Games and Economic Behavior, Elsevier, vol. 140(C), pages 88-98.
    9. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    10. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    cooperation; allocation; core; preconvexity; cohesiveness.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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