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

Listed author(s):
  • Ulrich Faigle

    ()

    (Universität zu Köln - Mathematisches Institut)

  • Michel Grabisch

    ()

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

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.

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File URL: https://halshs.archives-ouvertes.fr/halshs-00841259/document
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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00841259.

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Date of creation: Jun 2013
Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2013.52 - ISSN : 1955-611X. 2013
Handle: RePEc:hal:cesptp:halshs-00841259
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00841259
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  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. repec:hal:journl:halshs-00749950 is not listed on IDEAS
  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. repec:hal:cesptp:halshs-00749950 is not listed on IDEAS
  7. 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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