IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v225y2015i1p83-8910.1007-s10479-012-1226-y.html
   My bibliography  Save this article

The bargaining set for almost-convex games

Author

Listed:
  • Jesús Getán
  • Josep Izquierdo
  • Jesús Montes
  • Carles Rafels

Abstract

We generalize the well-known result of the coincidence of the bargaining set and the core for convex games (Maschler et al. 1972 ) to the class of games named almost-convex games, that is, coalitional games where all proper subgames are convex. Copyright Springer Science+Business Media, LLC 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:225:y:2015:i:1:p:83-89:10.1007/s10479-012-1226-y
    DOI: 10.1007/s10479-012-1226-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1226-y
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10479-012-1226-y?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
    2. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
    3. 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.
    4. Marina Núñez & Carles Rafels, 1998. "On extreme points of the core and reduced games," Annals of Operations Research, Springer, vol. 84(0), pages 121-133, December.
    5. Hamers, Herbert, 1997. "On the concavity of delivery games," European Journal of Operational Research, Elsevier, vol. 99(2), pages 445-458, June.
    6. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    7. Topkis, Donald M., 1987. "Activity optimization games with complementarity," European Journal of Operational Research, Elsevier, vol. 28(3), pages 358-368, March.
    8. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
    9. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    10. 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.
    11. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    12. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    13. Herbert Hamers & Flip Klijn & Bas Velzen, 2005. "On the Convexity of Precedence Sequencing Games," Annals of Operations Research, Springer, vol. 137(1), pages 161-175, July.
    14. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
    15. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    16. Einy, Ezra & Wettstein, David, 1996. "Equivalence between Bargaining Sets and the Core in Simple Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 65-71.
    17. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    18. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
    19. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    20. Marc Meertens & J. A. M. Potters & J. H. Reijnierse, 2007. "On Bargaining Sets In Symmetric Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 199-213.
    21. Herbert Hamers & Flip Klijn & Bas van Velzen, 2002. "On Games corresponding to Sequencing Situations with Precedence Relations," UFAE and IAE Working Papers 553.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    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. 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.

    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. 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.
    2. 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.
    3. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    4. 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.
    5. van Velzen, S. & Hamers, H.J.M., 2002. "On the Balancedness of Relaxed Sequencing Games," Discussion Paper 2002-49, Tilburg University, Center for Economic Research.
    6. 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.
    7. José-Manuel Giménez-Gómez & Peter Sudhölter & Cori Vilella, 2023. "Average monotonic cooperative games with nontransferable utility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 383-390, June.
    8. 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.
    9. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Other publications TiSEM ed1f8fce-da76-41a6-9a9e-9, Tilburg University, School of Economics and Management.
    10. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    11. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    12. Michela Chessa & Vito Fragnelli, 2014. "The bargaining set for sharing the power," Annals of Operations Research, Springer, vol. 215(1), pages 49-61, April.
    13. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    14. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    15. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Other publications TiSEM 3e1db5c9-0f77-4f91-a075-c, Tilburg University, School of Economics and Management.
    16. Ozen, U. & Norde, H.W. & Slikker, M., 2005. "On the Convexity of News Vendor Games," Other publications TiSEM 2faeeb88-8d0b-4c36-9b08-5, Tilburg University, School of Economics and Management.
    17. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Discussion Paper 2020-006, Tilburg University, Center for Economic Research.
    18. 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.
    19. Paula Corcho & José Ferreira, 2003. "Generalized externality games," Theory and Decision, Springer, vol. 54(2), pages 163-184, March.
    20. Avishay Aiche, 2019. "On the equal treatment imputations subset in the bargaining set for smooth vector-measure games with a mixed measure space of players," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 411-421, June.

    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:225:y:2015:i:1:p:83-89:10.1007/s10479-012-1226-y. 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.