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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)

  • Michel Grabisch

    (University of Paris I)

Abstract

The classical Shapley value is the average marginal contribution of a player, taken over all possible ways to form the grand coalition $$N$$ 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," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 189-199, November.
  • Handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0020-6
    DOI: 10.1007/s40505-013-0020-6
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    References listed on IDEAS

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    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. 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.
    3. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
    4. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
    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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    Cited by:

    1. Wang, Yaxian & Zhao, Zhenli & Baležentis, Tomas, 2023. "Benefit distribution in shared private charging pile projects based on modified Shapley value," Energy, Elsevier, vol. 263(PB).

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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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