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

Author

Listed:
  • Jacques-François Thisse

    (CERAS - Centre d'enseignement et de recherche en analyse socio-économique - ENPC - École des Ponts ParisTech, 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)

Abstract

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.

Suggested Citation

  • Jacques-François Thisse & Antoine Billot, 2005. "How to share when context matters : The Mobius value as a generalized solution for cooperative games," Post-Print halshs-00754051, HAL.
  • 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
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    References listed on IDEAS

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    1. repec:cor:louvrp:-1434 is not listed on IDEAS
    2. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.
    4. 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.
    5. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. Fabien Lange & Michel Grabisch, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
    7. 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.
    8. BILLOT, Antoine & THISSE, Jacques-François, 1999. "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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    Cited by:

    1. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
    2. Fabien Lange & László Kóczy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 281-292, July.
    3. repec:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500128 is not listed on IDEAS
    4. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    5. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.

    More about this item

    Keywords

    Shapley value; Quasivalue; Möbius inverse;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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