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

Author

Listed:
  • Ulrich Faigle

    () (Universität zu Köln - Mathematisches Institut)

  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00841259, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00841259
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00841259
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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. repec:hal:journl:halshs-00749950 is not listed on IDEAS
    5. 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.
    6. repec:hal:cesptp:halshs-00912889 is not listed on IDEAS
    7. 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.
    8. repec:hal:cesptp:halshs-00749950 is not listed on IDEAS
    9. 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)

    More about this item

    Keywords

    Coalitional game; coalition formation process; Shapley value; valeur de Shapley; processus de formation de coalition; Jeux coalitionnel;

    JEL classification:

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

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