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

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  • Ulrich Faigle

    (Universität zu Köln - Mathematisches Institut)

  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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    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.

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    Bibliographic Info

    Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00976923.

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    Date of creation: 2013
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    Publication status: Published, Economic Theory Bulletin, 2013, 189-199
    Handle: RePEc:hal:cesptp:halshs-00976923

    Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00976923
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    Related research

    Keywords: Coalitional game; coalition formation process; Shapley value;

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    1. Scafuri, Allen J & Yannelis, Nicholas C, 1984. "Non-symmetric Cardinal Value Allocations," Econometrica, Econometric Society, vol. 52(6), pages 1365-68, November.
    2. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Post-Print halshs-00749950, HAL.
    3. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00749950, HAL.
    4. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
    5. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-76, March.
    6. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-65, March.
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