IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v235y2015i1p301-31710.1007-s10479-015-1951-0.html
   My bibliography  Save this article

Autonomous coalitions

Author

Listed:
  • Stéphane Gonzalez
  • Michel Grabisch

Abstract

We consider in this paper solutions for TU-games where it is not assumed that the grand coalition is necessarily the final state of cooperation. Partitions of the grand coalition, or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation. The former case corresponds to the c-core, while the latter corresponds to the aspiration core or d-core, where in both case, the best configuration (called a maximising collection) is sought. We study maximising collections and characterize them with autonomous coalitions, that is, coalitions for which any solution of the d-core yields a payment for that coalition equal to its worth. In particular we show that the collection of autonomous coalitions is balanced, and that one cannot have at the same time a single possible payment (core element) and a single possible configuration. We also introduce the notion of inescapable coalitions, that is, those present in every maximising collection. We characterize the class of games for which the sets of autonomous coalitions, vital coalitions (in the sense of Shellshear and Sudhölter), and inescapable coalitions coincide, and prove that the set of games having a unique maximising coalition is dense in the set of games. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:301-317:10.1007/s10479-015-1951-0
    DOI: 10.1007/s10479-015-1951-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-015-1951-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-015-1951-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    3. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    4. Camelia Bejan & Juan Camilo Gómez, 2012. "Using The Aspiration Core To Predict Coalition Formation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-13.
    5. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
    6. Juan C. Cesco, 2012. "Nonempty Core-Type Solutions Over Balanced Coalitions In Tu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-16.
    7. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    8. Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
    9. Guesnerie, R. & Oddou, C., 1979. "On economic games which are not necessarily superadditive : Solution concepts and application to a local public good problem with few a agents," Economics Letters, Elsevier, vol. 3(4), pages 301-306.
    10. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395, Elsevier.
    11. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    12. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    13. Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
    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. Gonzalez, Stéphane & Rostom, Fatma Zahra, 2022. "Sharing the global outcomes of finite natural resource exploitation: A dynamic coalitional stability perspective," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 1-10.
    2. Stéphane Gonzalez & Aymeric Lardon, 2018. "Optimal deterrence of cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 207-227, March.
    3. Stéphane Gonzalez & Fatma Zahra Rostom, 2019. "Sharing the Global Benefits of Finite Natural Resource Exploitation: A Dynamic Coalitional Stability Perspective," Working Papers 1937, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    4. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.

    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. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    2. repec:hal:pseose:halshs-01235632 is not listed on IDEAS
    3. repec:hal:pseose:halshs-00881108 is not listed on IDEAS
    4. Camelia Bejan & Juan Camilo Gómez & Anne van den Nouweland, 2022. "On the importance of reduced games in axiomatizing core extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 637-668, October.
    5. Fatma Aslan & Papatya Duman & Walter Trockel, 2019. "Duality for General TU-games Redefined," Working Papers CIE 121, Paderborn University, CIE Center for International Economics.
    6. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    7. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
    8. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    9. Jingang Zhao, 2008. "The Maximal Payoff and Coalition Formation in Coalitional Games," Working Papers 2008.27, Fondazione Eni Enrico Mattei.
    10. Jingang Zhao, 2018. "A Reexamination of the Coase Theorem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 3(1), pages 111-132, December.
    11. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games," Documents de travail du Centre d'Economie de la Sorbonne 16081, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. repec:hal:pseose:hal-01372858 is not listed on IDEAS
    13. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Efficiency and Duality," Working Papers CIE 138, Paderborn University, CIE Center for International Economics.
    14. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    15. Michel Grabisch, 2016. "Rejoinder on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 335-337, July.
    16. Robert J. Aumann, 2007. "War and Peace," Chapters, in: Jean-Philippe Touffut (ed.), Augustin Cournot: Modelling Economics, chapter 5, Edward Elgar Publishing.
    17. Jean Guillaume Forand & Metin Uyanık, 2019. "Fixed-point approaches to the proof of the Bondareva–Shapley Theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 117-124, May.
    18. Michel Grabisch, 2016. "Rejoinder on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 335-337, July.
    19. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    20. Nobusumi Sagara & Milan Vlach, 2011. "A new class of convex games on σ-algebras and the optimal partitioning of measurable spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 617-630, August.
    21. Dylan Laplace Mermoud & Michel Grabisch & Peter Sudhölter, 2021. "Algorithmic aspects of core nonemptiness and core stability," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03354292, HAL.
    22. Vilella Bach, Misericòrdia, 2013. "The equity core and the core," Working Papers 2072/220760, Universitat Rovira i Virgili, Department of Economics.
    23. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.

    More about this item

    Keywords

    Cooperative game; Core; Balancedness; C-core; Aspiration core; Coalition formation; Autonomous coalitions; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    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:spr:annopr:v:235:y:2015:i:1:p:301-317:10.1007/s10479-015-1951-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.