IDEAS home Printed from https://ideas.repec.org/p/bar/bedcje/200275.html
   My bibliography  Save this paper

Coalitionally Monotonic Set-solutions for Cooperative TU Games

Author

Listed:
  • Josep Maria Izquierdo Aznar
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the trade-off between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core- selection requirement by the core-extension property.

Suggested Citation

  • Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:200275
    as

    Download full text from publisher

    File URL: http://www.ere.ub.es/dtreball/E0275.rdf/at_download/file
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    2. 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.
    3. Rafels, C. & Tijs, S.H., 1997. "On the cores of cooperative games and the stability of the Weber set," Other publications TiSEM 14435da8-14ce-4845-8e54-4, Tilburg University, School of Economics and Management.
    4. Daniel Granot & Michael Maschler, 1997. "The Reactive Bargaining Set: Structure, Dynamics and Extension to NTU Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 75-95.
    5. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 611-616.
    6. Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
    7. Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 61-73.
    8. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    9. Derks, J J M, 1992. "A Short Proof of the Inclusion of the Core in the Weber Set," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 149-150.
    10. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    11. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    12. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    13. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," 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 18, pages 591-667, Elsevier.
    14. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    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. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    2. J. Arin & V. Feltkamp, 2005. "Monotonicity properties of the nucleolus on the domain of veto balanced games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 331-341, December.
    3. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    4. Bezalel Peleg & Peter Sudhölter, 2015. "On Bargaining Sets of Convex NTU Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-7.
    5. J. Arin & V. Feltkamp & M. Montero, 2015. "A bargaining procedure leading to the serial rule in games with veto players," Annals of Operations Research, Springer, vol. 229(1), pages 41-66, June.
    6. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    7. Josep Maria Izquierdo & Carles Rafels, 2018. "The core and the steady bargaining set for convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 35-54, March.
    8. Jesús Getán & Josep Izquierdo & Jesús Montes & Carles Rafels, 2015. "The bargaining set for almost-convex games," Annals of Operations Research, Springer, vol. 225(1), pages 83-89, February.
    9. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
    10. Josep Maria Izquierdo & Carlos Rafels, 2017. "The incentive core in co-investment problems," UB School of Economics Working Papers 2017/369, University of Barcelona School of Economics.
    11. Josep Maria Izquierdo Aznar, 2003. "Regular Population Monotonic Allocation Schemes and the Core," Working Papers in Economics 110, Universitat de Barcelona. Espai de Recerca en Economia.
    12. Vilella Bach, Misericòrdia, 2013. "The equity core and the core," Working Papers 2072/220760, Universitat Rovira i Virgili, Department of Economics.
    13. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    14. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    15. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    16. Emilio Calvo, 2021. "Redistribution of tax resources: a cooperative game theory approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(4), pages 633-686, December.
    17. Ezra Einy & Diego Moreno & Benyamin Shitovitz, 2005. "The bargaining set of a large economy with differential information," Studies in Economic Theory, in: Dionysius Glycopantis & Nicholas C. Yannelis (ed.), Differential Information Economies, pages 541-552, Springer.
    18. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    19. Cori Vilella, 2014. "The equity core and the core," Economics Bulletin, AccessEcon, vol. 34(1), pages 313-323.
    20. Josep Izquierdo & Carles Rafels, 2012. "A characterization of convex TU games by means of the Mas-Colell bargaining set (à la Shimomura)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 381-395, May.

    More about this item

    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:bar:bedcje:200275. 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: Espai de Recerca en Economia (email available below). General contact details of provider: https://edirc.repec.org/data/feubaes.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.