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A Concise Axiomatization of a Shapley-type Value for Stochastic Coalition Processes

Author

Listed:
  • Ulrich Faigle

    (Universität zu Köln)

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

Abstract

The classical Shapley value is 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 coalition formation model 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 only slightly weaker than the original one but allows a much more transparent proof. Moreover, the logical independence of the axioms is exhibited.

Suggested Citation

  • Ulrich Faigle & Michel Grabisch, 2013. "A Concise Axiomatization of a Shapley-type Value for Stochastic Coalition Processes," Post-Print halshs-00976923, HAL.
  • Handle: RePEc:hal:journl:halshs-00976923
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00976923
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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, 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.
    4. 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.
    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.
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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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