IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-04571264.html
   My bibliography  Save this paper

Stable outcomes in simple cooperative games

Author

Listed:
  • Gabrielle Demange

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

In a cooperative game, coalitions are the fundamental behavioral units. Stable outcomes (in the core) are those blocked by no coalition. This paper has two objectives. First, building on the notion of intermediate preferences indexed by a median graph, I unify and extend previous results on the existence of stable outcomes in simple games. Second, I review how and when the core approach applies in more general settings and may help to predict the stable splitting of a whole group into disjoint coalitions.

Suggested Citation

  • Gabrielle Demange, 2024. "Stable outcomes in simple cooperative games," Post-Print halshs-04571264, HAL.
    • Handle: RePEc:hal:journl:halshs-04571264
    DOI: 10.1016/j.jmateco.2024.102960
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    3. Hansen, Pierre & Thisse, Jacques-Francois, 1981. "Outcomes of voting and planning : Condorcet, Weber and Rawls locations," Journal of Public Economics, Elsevier, vol. 16(1), pages 1-15, August.
    4. Demange, Gabrielle & Henriet, Dominique, 1991. "Sustainable oligopolies," Journal of Economic Theory, Elsevier, vol. 54(2), pages 417-428, August.
    5. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    6. Currarini, Sergio, 2007. "Group stability of hierarchies in games with spillovers," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 187-202, December.
    7. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August.
    8. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
    9. Eric Weese, 2015. "Political mergers as coalition formation: An analysis of the Heisei municipal amalgamations," Quantitative Economics, Econometric Society, vol. 6(2), pages 257-307, July.
    10. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    11. Morelli, Massimo & Park, In-Uck, 2016. "Internal hierarchy and stable coalition structures," Games and Economic Behavior, Elsevier, vol. 96(C), pages 90-96.
    12. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    13. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    14. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    15. Gabrielle Demange & Wooders Myrna, 2005. "Group Formation in Economics: Networks, Clubs and Coalitions," Post-Print halshs-00576778, HAL.
    16. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    17. Greenberg Joseph & Weber Shlomo, 1993. "Stable Coalition Structures with a Unidimensional Set of Alternatives," Journal of Economic Theory, Elsevier, vol. 60(1), pages 62-82, June.
    18. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
    19. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    20. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    21. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    22. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    23. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    24. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.
    25. Carraro, Carlo & Siniscalco, Domenico, 1993. "Strategies for the international protection of the environment," Journal of Public Economics, Elsevier, vol. 52(3), pages 309-328, October.
    26. Klaus Desmet & Michel Breton & Ignacio Ortuño-Ortín & Shlomo Weber, 2011. "The stability and breakup of nations: a quantitative analysis," Journal of Economic Growth, Springer, vol. 16(3), pages 183-213, September.
    27. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    28. Andrea Robbett, 2015. "Voting with hands and feet: the requirements for optimal group formation," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 522-541, September.
    29. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    30. Edith Elkind & Martin Lackner & Dominik Peters, 2022. "Preference Restrictions in Computational Social Choice: A Survey," Papers 2205.09092, arXiv.org.
    31. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    32. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    33. Yi, Sang-Seung, 1997. "Stable Coalition Structures with Externalities," Games and Economic Behavior, Elsevier, vol. 20(2), pages 201-237, August.
    34. Wooders, Myrna, 1978. "Equilibria, the core, and jurisdiction structures in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 18(2), pages 328-348, August.
    Full references (including those not matched with items on IDEAS)

    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. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.
    2. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, September.
    3. Fan‐Chin Kung, 2006. "An Algorithm for Stable and Equitable Coalition Structures with Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(3), pages 345-355, August.
    4. Alexander Kovalenkov & Myrna Wooders, 2003. "Advances in the theory of large cooperative games and applications to club theory; the side payments case," Chapters, in: Carlo Carraro (ed.), The Endogenous Formation of Economic Coalitions, chapter 1, Edward Elgar Publishing.
    5. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    6. Marco A. Marini, 2007. "An Overview of Coalitions and Networks Formation Models for Economic Applications," Working Papers 0707, CREI Università degli Studi Roma Tre, revised 2007.
    7. Le Breton, Michel & Weber, Shlomo, 2004. "Group Formation with Heterogeneous Sets," IDEI Working Papers 288, Institut d'Économie Industrielle (IDEI), Toulouse.
    8. Marco Marini, 2007. "An Overview of Coalition & Network Formation Models for Economic Applications," Working Papers 0712, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    9. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Debasis Mishra & A. Talman, 2010. "A characterization of the average tree solution for tree games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 105-111, March.
    11. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    12. Sergio Currarini, 2003. "On the Stability of Hierarchies in Games with Externalities," Working Papers 2003.19, Fondazione Eni Enrico Mattei.
    13. Fan-Chin Kung, 2010. "Coalition formation with local public goods and group-size effect," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 573-583, October.
    14. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010. "The average tree solution for cooperative games with communication structure," Games and Economic Behavior, Elsevier, vol. 68(2), pages 626-633, March.
    15. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    16. Clemens Puppe & Arkadii Slinko, 2019. "Condorcet domains, median graphs and the single-crossing property," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 285-318, February.
    17. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    18. Fan-chin Kung, 2005. "Coalition Formation with Local Public Goods and Network Effect," Game Theory and Information 0506007, University Library of Munich, Germany.
    19. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    20. Hans‐Peter Weikard, 2009. "Cartel Stability Under An Optimal Sharing Rule," Manchester School, University of Manchester, vol. 77(5), pages 575-593, September.

    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:hal:journl:halshs-04571264. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.