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A Note on Values for Markovian 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. The authors have proposed in a previous paper 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 at the grand coalition. The aim of this note is to develop some explanations in the general context of time discrete stochastic processes, exhibit new properties of the model, correct some inaccuracies in the original paper, and give a new version of the axiomatization.

Suggested Citation

  • Ulrich Faigle & Michel Grabisch, 2013. "A Note on Values for Markovian Coalition Processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00912889, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00912889
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00912889
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    References listed on IDEAS

    as
    1. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
    2. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
    3. 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.
    4. repec:hal:pseose:halshs-00749950 is not listed on IDEAS
    5. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    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)

    Citations

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    Cited by:

    1. 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.
    2. Ulrich Faigle & Michel Grabisch, 2013. "A concise axiomatization of a Shapley-type value for stochastic coalition processes," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 189-199, November.
    3. repec:hal:pseose:halshs-01207823 is not listed on IDEAS

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    More about this item

    Keywords

    coalitional game; coalition formation process; Shapley value;
    All these keywords.

    JEL classification:

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

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