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How to share when context matters : The Mobius value as a generalized solution for cooperative games

Listed author(s):
  • Jacques-François Thisse

    (CERAS - Centre d'enseignement et de recherche en analyse socio-économique - École des Ponts ParisTech (ENPC), CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain)

  • Antoine Billot

    (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain, UP2 - Université Panthéon-Assas - M.E.N.E.S.R. - Ministère de l'Éducation nationale, de l’Enseignement supérieur et de la Recherche)

All quasivalues rest on a set of three basic axioms (efficiency, null player, and additivity), which are augmented with positivity for random order values, and with positivity and partnership for weighted values. We introduce the concept of Möbius value associated with a sharing system and show that this value is characterized by the above three axioms. We then establish that (i) a Möbius value is a random order value if and only if the sharing system is stochastically rationalizable and (ii) a Möbius value is a weighted value if and only if the sharing system satisfies the Luce choice axiom.

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Paper provided by HAL in its series Post-Print with number halshs-00754051.

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Date of creation: Dec 2005
Publication status: Published in Journal of Mathematical Economics, Elsevier, 2005, 41 (8), pp.1007-1029. <10.1016/j.jmateco.2004.12.008>
Handle: RePEc:hal:journl:halshs-00754051
DOI: 10.1016/j.jmateco.2004.12.008
Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754051
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. repec:cor:louvrp:-1434 is not listed on IDEAS
  2. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  3. Michel Grabisch & Fabien Lange, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
  4. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
  6. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076 Elsevier.
  7. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
  8. BILLOT, Antoine & THISSE, Jacques-François, "undated". "A discrete choice model when context matters," CORE Discussion Papers RP 1434, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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