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The Shapley Value and Average Convex Games

Author

Listed:
  • Inarra, Elena
  • Usategui, Jose M

Abstract

In this paper we reformulate the necessary and sufficient conditions for the Shapley value to lie in the core of the game. Two new classes of games, which strictly include convex games, are introduced: average convex games and partially average convex games. Partially average convex games, which need not be superadditive, include average convex games. The Shapley value of a game for both classes is in the core. Some Cobb Douglas production games with increasing returns to scale turn out to be average convex games. The paper concludes with a comparison between the new classes of games introduced and some previous extensions of the convexity notion.

Suggested Citation

  • Inarra, Elena & Usategui, Jose M, 1993. "The Shapley Value and Average Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(1), pages 13-29.
    • Handle: RePEc:spr:jogath:v:22:y:1993:i:1:p:13-29
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    Citations

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    Cited by:

    1. Skoda, Alexandre & Venel, Xavier, 2023. "Weighted average-convexity and Shapley values," Games and Economic Behavior, Elsevier, vol. 140(C), pages 88-98.
    2. Slikker, M., 1998. "Average Convexity in Communication Situations," Other publications TiSEM 612b0000-a66a-435a-a707-2, Tilburg University, School of Economics and Management.
    3. Shoshana Anily, 2018. "Full characterization of the nonnegative core of some cooperative games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 303-316, June.
    4. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    5. Corcho, Paula, 1996. "Generalized externality games: economic applications," UC3M Working papers. Economics 3979, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Alexandre Skoda & Xavier Venel, 2022. "Weighted Average-convexity and Cooperative Games," Documents de travail du Centre d'Economie de la Sorbonne 22016, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Zhao, Jingang, 1999. "A necessary and sufficient condition for the convexity in oligopoly games," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 189-204, March.
    8. Alexandre Skoda & Xavier Venel, 2022. "Weighted Average-convexity and Cooperative Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03717539, HAL.
    9. Driessen, Theo S.H. & Meinhardt, Holger I., 2005. "Convexity of oligopoly games without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 102-126, July.
    10. Takaaki Abe & Satoshi Nakada, 2023. "Core stability of the Shapley value for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 523-543, May.
    11. Slikker, M., 1998. "Average Convexity in Communication Situations," Discussion Paper 1998-12, Tilburg University, Center for Economic Research.
    12. Alexandre Skoda & Xavier Venel, 2022. "Weighted Average-convexity and Cooperative Games," Post-Print halshs-03717539, HAL.
    13. Takaaki Abe & Satoshi Nakada, 2018. "Generalized Potentials, Value, and Core," Discussion Paper Series DP2018-19, Research Institute for Economics & Business Administration, Kobe University.

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