IDEAS home Printed from https://ideas.repec.org/p/zbw/rwirep/236.html
   My bibliography  Save this paper

Outside Options in Probabilistic Coalition Situations

Author

Listed:
  • Belau, Julia

Abstract

In this paper, I introduce an extension of (TU) games with a coalition structure. Taking a situation where all coalitions are already established is not reasonable in order to forecast the reality; there is not only one possible coalition, there are several. I consider situations where coalitions are not established yet and take into account the likelihood of each possible coalition. This leads to a generalized, probabilistic setting for coalition structures. Probabilistic versions of known axioms are introduced as well as new probabilistic axioms. Generalizations of both the outside-option-sensitive chi-value (Casajus, Soc Choice Welf 32, 1-13, 2009) and its outside-option-insensitive pendant, the component restricted Shapley value (Aumann and Drèze, Int. J. Game Theory 3, 217-237, 1974), are defined and axiomatic characterizations are given.

Suggested Citation

  • Belau, Julia, 2011. "Outside Options in Probabilistic Coalition Situations," Ruhr Economic Papers 236, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    • Handle: RePEc:zbw:rwirep:236
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/45306/1/655957960.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. 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).
    3. Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
    4. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 1-13, January.
    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. Julia Belau, 2013. "An outside-option-sensitive allocation rule for networks: the kappa-value," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 175-188, November.
    2. Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    3. Tobias Hiller, 2022. "Allocation of portfolio risk and outside options," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(7), pages 2845-2848, October.
    4. repec:zbw:rwirep:0326 is not listed on IDEAS
    5. repec:zbw:rwirep:0456 is not listed on IDEAS
    6. Julia Belau, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 0326, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    7. Julia Belau, 2013. "Effi cient Formulas and Computational Efficiency for Glove Games," Ruhr Economic Papers 0456, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    8. Belau, Julia, 2013. "Efficient Formulas and Computational Efficiency for Glove Games," Ruhr Economic Papers 456, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    9. Belau, Julia, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 326, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.

    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. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    2. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    3. González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    4. Julia Belau, 2011. "Outside Options in Probabilistic Coalition Situations," Ruhr Economic Papers 0236, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    5. Daniel Li Li & Erfang Shan, 2022. "Safety of links with respect to the Myerson value for communication situations," Operational Research, Springer, vol. 22(3), pages 2121-2131, July.
    6. Daniel Li Li & Erfang Shan, 2021. "Cooperative games with partial information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 297-309, March.
    7. repec:zbw:rwirep:0236 is not listed on IDEAS
    8. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    9. Tejada, O. & Álvarez-Mozos, M., 2018. "Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 114-122.
    10. Joosung Lee, 2015. "Multilateral Bargaining in Networks: On the Prevalence of Inefficiencies," Working Papers 2015.53, Fondazione Eni Enrico Mattei.
    11. Sylvain Béal & Anna Khmelnitskaya & Philippe Solal, 2018. "Two-step values for games with two-level communication structure," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 563-587, February.
    12. Elena Parilina & Artem Sedakov, 2016. "Stable Cooperation in a Game with a Major Player," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-20, June.
    13. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    14. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    15. van den Brink, J.R., 1999. "An Axiomatization of the Shapley Value Using a Fairness Property," Other publications TiSEM 0090365c-9bab-4367-b660-5, Tilburg University, School of Economics and Management.
    16. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    17. S. Béal & A. Lardon & E. Rémila & P. Solal, 2012. "The average tree solution for multi-choice forest games," Annals of Operations Research, Springer, vol. 196(1), pages 27-51, July.
    18. René Brink & Anna Khmelnitskaya & Gerard Laan, 2016. "An Owen-type value for games with two-level communication structure," Annals of Operations Research, Springer, vol. 243(1), pages 179-198, August.
    19. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    20. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    21. Julia Belau, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 0326, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

    More about this item

    Keywords

    TU game; coalition structure; outside option;
    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:zbw:rwirep:236. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/rwiesde.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.