IDEAS home Printed from https://ideas.repec.org/p/gat/wpaper/2019.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: ftp://ftp.gate.cnrs.fr/RePEc/2020/2019.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thoron, Sylvie & Sol, Emmanuel & Willinger, Marc, 2009. "Do binding agreements solve the social dilemma?," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1271-1282, December.
    2. Marc Escrihuela-Villar, 2009. "A note on cartel stability and endogenous sequencing with tacit collusion," Journal of Economics, Springer, vol. 96(2), pages 137-147, March.
    3. Berglöf, Erik & Burkart, Mike & Friebel, Guido & Paltseva, Elena, 2012. "Club-in-the-club: Reform under unanimity," Journal of Comparative Economics, Elsevier, vol. 40(3), pages 492-507.
    4. Argenton, Cédric, 2019. "Colluding on excluding," European Economic Review, Elsevier, vol. 113(C), pages 194-206.
    5. Davide Dragone, 2007. "Should One Sell Domestic Firms to Foreign Ones? A Tale of Delegation, Acquisition and Collusion," Rivista di Politica Economica, SIPI Spa, vol. 97(3), pages 85-112, May-June.
    6. Mariana Cunha & Paula Sarmento, 2014. "Does Vertical Integration Promote Downstream Incomplete Collusion? An Evaluation of Static and Dynamic Stability," Journal of Industry, Competition and Trade, Springer, vol. 14(1), pages 1-38, March.
    7. Karp, Larry & Simon, Leo, 2013. "Participation games and international environmental agreements: A non-parametric model," Journal of Environmental Economics and Management, Elsevier, vol. 65(2), pages 326-344.
    8. Thoron, Sylvie, 2004. "Which acceptable agreements are equilibria?," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 111-134, January.
    9. Takaaki Abe, 2019. "Cartel formation in Cournot competition with asymmetric costs: A partition function approach," Working Papers 1911, Waseda University, Faculty of Political Science and Economics.
    10. Ludwig Auer & Tu Anh Pham, 2021. "Optimal destabilization of cartels," Journal of Regulatory Economics, Springer, vol. 59(2), pages 175-192, April.
    11. Olaizola Ortega, María Norma, 2003. "An Approach to the stability of international environmental agreements: the absorbing sets solution," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    12. Achim Hagen & Pierre von Mouche & Hans-Peter Weikard, 2020. "The Two-Stage Game Approach to Coalition Formation: Where We Stand and Ways to Go," Games, MDPI, vol. 11(1), pages 1-31, January.
    13. Mao, Liang, 2017. "Designing International Environmental Agreements under Participation Uncertainty," MPRA Paper 86248, University Library of Munich, Germany.
    14. Marc Escrihuela-Villar, 2009. "Does cartel leadership facilitate collusion?," DEA Working Papers 39, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    15. Olaizola Ortega, María Norma & Kuipers, Jerome, 2004. "Internal Organization of Firms and Cartel Formation," IKERLANAK 2004-15, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    16. Takaaki Abe, 2021. "Cartel Formation in Cournot Competition with Asymmetric Costs: A Partition Function Approach," Games, MDPI, vol. 12(1), pages 1-16, February.
    17. Georg Clemens & Holger A. Rau, 2022. "Either with us or against us: experimental evidence on partial cartels," Theory and Decision, Springer, vol. 93(2), pages 237-257, September.
    18. María Gómez-Rúa & Juan Vidal-Puga, 2014. "Bargaining and membership," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 800-814, July.
    19. Effrosyni Diamantoudi & Eftichios Sartzetakis, 2015. "International environmental agreements: coordinated action under foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 527-546, August.
    20. Marette, S. & Crepsi, J.M., 1999. "Cartel Stability and Quality Signaling," Papers 99-29, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gat:wpaper:2019. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nelly Wirth (email available below). General contact details of provider: https://edirc.repec.org/data/gateefr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.