IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2020i46p12-29.html

Shapley's value and its axiomatization in games with prior probabilities of coalition formation

Author

Listed:
  • Kamionko, V.

    (Novosibirsk State University, Novosibirsk, Russia)

  • Marakulin, V.

    (Novosibirsk State University, Novosibirsk, Russia
    Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia)

Abstract

A new, generalized model of a cooperative game with transferable utility (TP game) is introduced and studied, in which, in addition to the characteristic function, two additional functions are used: relations between players and the probability of coalition formation, which reflect the main features of the interaction of people in specific groups. Various properties of the probability function are studied, and it is proved which of them are sufficient for its transformation into a probability measure. The generalized Shapley vector is defined for a new class of games as the mathematical expectation of a player from his marginal contribution to coalitions. Necessary and sufficient conditions are given for the generalized Shapley vector to completely coincide with the classical one introduced by Shapley himself. An axiomatization of value functions on a new class of games is proposed, which is also an extension of existing axioms in original TP games. It is proved that the (generalized) Shapley vector and only it corresponds to the introduced axioms.

Suggested Citation

  • Kamionko, V. & Marakulin, V., 2020. "Shapley's value and its axiomatization in games with prior probabilities of coalition formation," Journal of the New Economic Association, New Economic Association, vol. 46(2), pages 12-29.
    • Handle: RePEc:nea:journl:y:2020:i:46:p:12-29
    DOI: 10.31737/2221-2264-2020-46-2-1
    as

    Download full text from publisher

    File URL: http://www.econorus.org/repec/journl/2020-46-12-29r.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.31737/2221-2264-2020-46-2-1?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
    ---><---

    References listed on IDEAS

    as
    1. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, Enero-Abr.
    2. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076, Elsevier.
    3. Fuad Aleskerov & Manfred Holler & Rita Kamalova, 2014. "Power distribution in the Weimar Reichstag in 1919–1933," Annals of Operations Research, Springer, vol. 215(1), pages 25-37, April.
    4. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054, Elsevier.
    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. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.

    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. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "The Consistent Coalitional Value," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 832-851, November.
    2. Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    3. Barr, Jason & Passarelli, Francesco, 2009. "Who has the power in the EU?," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 339-366, May.
    4. Xingwei Hu, 2018. "A Theory of Dichotomous Valuation with Applications to Variable Selection," Papers 1808.00131, arXiv.org, revised Mar 2020.
    5. Giulia Bernardi & Josep Freixas, 2018. "The Shapley value analyzed under the Felsenthal and Machover bargaining model," Public Choice, Springer, vol. 176(3), pages 557-565, September.
    6. Xingwei Hu, 2020. "A theory of dichotomous valuation with applications to variable selection," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1075-1099, November.
    7. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    8. Ünsal Özdilek, 2020. "Land and building separation based on Shapley values," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 6(1), pages 1-13, December.
    9. Lyu, Xiaohuan & Lalla-Ruiz, Eduardo & Schulte, Frederik, 2025. "The collaborative berth allocation problem with row-generation algorithms for stable cost allocations," European Journal of Operational Research, Elsevier, vol. 323(3), pages 888-906.
    10. Barbaro, Salvatore, 2025. "Election methods and political polarization," Mathematical Social Sciences, Elsevier, vol. 135(C).
    11. Harald Wiese, 2012. "Values with exogenous payments," Theory and Decision, Springer, vol. 72(4), pages 485-508, April.
    12. Antonin Macé, 2017. "Voting with evaluations: characterizations of evaluative voting and range voting," Working Papers halshs-01222200, HAL.
    13. Can, Burak & Leth Hougaard, Jens & Pourpouneh, Mohsen, 2022. "On reward sharing in blockchain mining pools," Games and Economic Behavior, Elsevier, vol. 136(C), pages 274-298.
    14. Ekaterina Marova & Ekaterina Gromova & Polina Barsuk & Anastasia Shagushina, 2020. "On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    15. repec:aen:journl:ej36-4-egerer is not listed on IDEAS
    16. Reiner Wolff, 2007. "Eine spieltheoretische Analyse des Länderfinanzausgleichs in der Bundesrepublik Deutschland," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 27(1), pages 89-101, February.
    17. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    18. Barbaro Salvatore, 2025. "Wie sollten wir unseren Bundestag wählen?," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 26(4), pages 472-480.
    19. Justin Yifu Lin, 2007. "Development and Transition : Idea, Strategy, and Viability," Development Economics Working Papers 22709, East Asian Bureau of Economic Research.
    20. Jens Leth Hougaard & Kurt Nielsen & Athanasios Papakonstantinou, 2013. "A Multi-attribute Yardstick Auction without Prior Scoring," MSAP Working Paper Series 02_2013, University of Copenhagen, Department of Food and Resource Economics, revised Mar 2014.
    21. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:nea:journl:y:2020:i:46:p:12-29. 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: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.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.