IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00841259.html
   My bibliography  Save this paper

A concise axiomatization of a Shapley-type value for stochastic coalition processes

Author

Listed:
  • Ulrich Faigle

    (Universität zu Köln = University of Cologne)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition N when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general model of coalition formation where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is weaker than the one in the original paper but allows a much more transparent correctness proof. Moreover, the logical independence of the axioms is proved.

Suggested Citation

  • Ulrich Faigle & Michel Grabisch, 2013. "A concise axiomatization of a Shapley-type value for stochastic coalition processes," Post-Print halshs-00841259, HAL.
  • Handle: RePEc:hal:journl:halshs-00841259
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00841259
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-00841259/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    2. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
    3. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
    4. Ulrich Faigle & Michel Grabisch, 2013. "A note on values for Markovian coalition processes," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 111-122, November.
    5. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    6. Scafuri, Allen J & Yannelis, Nicholas C, 1984. "Non-symmetric Cardinal Value Allocations," Econometrica, Econometric Society, vol. 52(6), pages 1365-1368, November.
    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. Ulrich Faigle & Michel Grabisch, 2013. "A note on values for Markovian coalition processes," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 111-122, November.
    2. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    3. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    4. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    5. Dietzenbacher, Bas & Yanovskaya, Elena, 2022. "The equal split-off set for NTU-games," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Other publications TiSEM b1bf227f-53df-4fad-93b8-8, Tilburg University, School of Economics and Management.
    7. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    8. Swanenberg, A.J.M., 1981. "Rationing and price dynamics in a simple market-game," Research Memorandum FEW 97, Tilburg University, School of Economics and Management.
    9. Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
    10. Swanenberg, A.J.M., 1981. "Rationing and price dynamics in a simple market-game," Other publications TiSEM 43559370-0b7a-4bd0-87ed-6, Tilburg University, School of Economics and Management.
    11. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    12. Vidal-Puga, Juan J., 2008. "Forming coalitions and the Shapley NTU value," European Journal of Operational Research, Elsevier, vol. 190(3), pages 659-671, November.
    13. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    14. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    15. Grabisch, Michel & Sudhölter, Peter, 2018. "On a class of vertices of the core," Games and Economic Behavior, Elsevier, vol. 108(C), pages 541-557.
    16. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, vol. 235(3), pages 709-717.
    17. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    18. J. Bilbao & A. Jiménez-Losada & E. Lebrón & S. Tijs, 2002. "Theτ-value for games on matroids," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 67-81, June.
    19. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    20. Lange, Fabien & Grabisch, Michel, 2009. "Values on regular games under Kirchhoff's laws," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 322-340, November.

    More about this item

    Keywords

    Coalitional game; coalition formation process; Shapley value; Jeux coalitionnel; processus de formation de coalition; valeur de Shapley;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:halshs-00841259. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.