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On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations

Author

Listed:
  • Dongshuang Hou

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China)

  • Aymeric Lardon

    (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint Etienne, France)

  • Hao Sun

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China)

Abstract

Two new notions of stability of coalitions, based on the idea of exclusion or integration of players depending on how they affect allocations, are introduced for cooperative transferable utility games. The first one, called internal stability, requires that no coalition member would find that her departure from the coalition would improve her allocation or those of all her partners. The second one, called external stability, requires that coalitions members do not wish to recruit a new partner willing to join the coalition, since her arrival would hurt some of them. As an application of these two notions, we study the stability of Group Purchasing Organizations using the Shapley value to allocate costs between buyers. Our main results suggest that, when all buyers are initially alone, while small buyers will form internally and externally stable Group Purchasing Organizations to benefit from the best price discount, big buyers will be mutually exclusive and may cooperate with only small buyers.

Suggested Citation

  • Dongshuang Hou & Aymeric Lardon & Hao Sun, 2020. "On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations," Working Papers 2019, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    • Handle: RePEc:gat:wpaper:2019
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    References listed on IDEAS

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    1. Sylvie Thoron, 1998. "Formation of a Coalition-Proof Stable Cartel," Canadian Journal of Economics, Canadian Economics Association, vol. 31(1), pages 63-76, February.
    2. Schotanus, Fredo & Telgen, Jan & de Boer, Luitzen, 2008. "Unfair allocation of gains under the Equal Price allocation method in purchasing groups," European Journal of Operational Research, Elsevier, vol. 187(1), pages 162-176, May.
    3. Yang, Yu-Chen & Cheng, Hsing Kenneth & Ding, Chao & Li, Shengli, 2017. "To join or not to join group purchasing organization: A vendor's decision," European Journal of Operational Research, Elsevier, vol. 258(2), pages 581-589.
    4. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    5. Claude d'Aspremont & Alexis Jacquemin & Jean Jaskold Gabszewicz & John A. Weymark, 1983. "On the Stability of Collusive Price Leadership," Canadian Journal of Economics, Canadian Economics Association, vol. 16(1), pages 17-25, February.
    6. LI, Li, 2019. "Cooperative purchasing and preactive inventory sharing – Channel balancing and performance improvement," European Journal of Operational Research, Elsevier, vol. 278(3), pages 738-751.
    7. Doucette, William R., 1997. "Influences on member commitment to group purchasing organizations," Journal of Business Research, Elsevier, vol. 40(3), pages 183-189, November.
    8. Hou, Dongshuang & Sun, Hao & Sun, Panfei & Driessen, Theo, 2018. "A note on the Shapley value for airport cost pooling game," Games and Economic Behavior, Elsevier, vol. 108(C), pages 162-169.
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    Cited by:

    1. Emmerling, Johannes & Tavoni, Massimo & Pezzoli, Perguiseppe, 2023. "SRM on the Table: The Role of Geoengineering for the Stability and Effectiveness of Climate Coalitions," RFF Working Paper Series 23-32, Resources for the Future.
    2. Piergiuseppe Pezzoli & Johannes Emmerling & Massimo Tavoni, 2023. "SRM on the table: the role of geoengineering for the stability and effectiveness of climate coalitions," Climatic Change, Springer, vol. 176(10), pages 1-21, October.

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    More about this item

    Keywords

    Internal and external stability; Group purchasing organization; Cost allocation; Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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