IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v93y2022i4d10.1007_s11238-022-09865-0.html
   My bibliography  Save this article

Optimization implementation of solution concepts for cooperative games with stochastic payoffs

Author

Listed:
  • Panfei Sun

    (Northwestern Polytechnical University)

  • Dongshuang Hou

    (Northwestern Polytechnical University)

  • Hao Sun

    (Northwestern Polytechnical University)

Abstract

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. Inspired by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models.

Suggested Citation

  • Panfei Sun & Dongshuang Hou & Hao Sun, 2022. "Optimization implementation of solution concepts for cooperative games with stochastic payoffs," Theory and Decision, Springer, vol. 93(4), pages 691-724, November.
    • Handle: RePEc:kap:theord:v:93:y:2022:i:4:d:10.1007_s11238-022-09865-0
    DOI: 10.1007/s11238-022-09865-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-022-09865-0
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-022-09865-0?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
    2. Luis Ruiz & Federico Valenciano & José Zarzuelo, 1998. "Some new results on least square values for TU games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 139-158, June.
    3. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    6. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
    7. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    8. Suijs, J.P.M. & Borm, P.E.M., 1996. "Cooperative Games with Stochastic Payoffs : Determanistic Equivalents," Research Memorandum 713, Tilburg University, School of Economics and Management.
    9. Dongshuang Hou & Panfei Sun & Genjiu Xu & Theo Driessen, 2018. "Compromise for the complaint: an optimization approach to the ENSC value and the CIS value," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(4), pages 571-579, April.
    10. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    11. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    12. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    13. F. R. Fernández & J. Puerto & M. J. Zafra, 2002. "Cores Of Stochastic Cooperative Games With Stochastic Orders," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 265-280.
    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. Meinhardt, Holger Ingmar, 2021. "Disentangle the Florentine Families Network by the Pre-Kernel," MPRA Paper 106482, University Library of Munich, Germany.
    2. Wenna Wang & Hao Sun & Rene (J.R.) van den Brink & Genjiu Xu, 2018. "The family of ideal values for cooperative games," Tinbergen Institute Discussion Papers 18-002/II, Tinbergen Institute.
    3. Wenna Wang & Hao Sun & René Brink & Genjiu Xu, 2019. "The Family of Ideal Values for Cooperative Games," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1065-1086, March.
    4. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    5. Alexander Karpov & Semyon Yurkov, 2012. "Generalized bankruptcy problem," HSE Working papers WP BRP 08/FE/2012, National Research University Higher School of Economics.
    6. Hou, Dongshuang & Lardon, Aymeric, 2020. "An Optimization Characterization of the upper optimal complaint value," Economics Letters, Elsevier, vol. 186(C).
    7. Panfei Sun & Dongshuang Hou & Hao Sun & Theo Driessen, 2017. "Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 336-352, April.
    8. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    9. H. Andrew Michener & Daniel J. Myers, 1998. "Probabilistic Coalition Structure Theories," Journal of Conflict Resolution, Peace Science Society (International), vol. 42(6), pages 830-860, December.
    10. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    11. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
    12. Tamas Solymosi & Balazs Sziklai, 2015. "Universal Characterization Sets for the Nucleolus in Balanced Games," CERS-IE WORKING PAPERS 1512, Institute of Economics, Centre for Economic and Regional Studies.
    13. Panfei Sun & Dongshuang Hou & Hao Sun & Hui Zhang, 2017. "Process and optimization implementation of the $$\alpha $$ α -ENSC value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 293-308, October.
    14. Meinhardt, Holger Ingmar, 2020. "On the Replication of the Pre-Kernel and Related Solutions," MPRA Paper 102676, University Library of Munich, Germany.
    15. Samuel Ferey & Pierre Dehez, 2016. "Multiple Causation, Apportionment, and the Shapley Value," The Journal of Legal Studies, University of Chicago Press, vol. 45(1), pages 143-171.
    16. Toru Hokari & Yukihiko Funaki & Peter Sudhölter, 2020. "Consistency, anonymity, and the core on the domain of convex games," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 187-197, December.
    17. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    18. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2021. "Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    19. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    20. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, 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:kap:theord:v:93:y:2022:i:4:d:10.1007_s11238-022-09865-0. 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.