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Variations on the shapley value

In: Handbook of Game Theory with Economic Applications

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  • Monderer, Dov
  • Samet, Dov

Abstract

This survey captures the main contributions in the area described by the title that were published up to 1997. (Unfortunately, it does not capture all of them.) The variations that are the subject of this chapter are those axiomatically characterized solutions which are obtained by varying either the set of axioms that define the Shapley value, or the domain over which this value is defined, or both.In the first category, we deal mainly with probabilistic values. These are solutions that preserve one of the essential features of the Shapley value, namely, that they are given, for each player, by some averaging of the player's marginal contributions to coalitions, where the probabilistic weights depend on the coalitions only and not on the game. The Shapley value is the unique probabilistic value that is efficient and symmetric. We characterize and discuss two families of solutions: quasivalues, which are efficient probabilistic values, and semivalues, which are symmetric probabilistic values.In the second category, we deal with solutions that generalize the Shapley value by changing the domain over which the solution is defined. In such generalizations the solution is defined on pairs, consisting of a game and some structure on the set of players. The Shapley value is a special case of such a generalization in the sense that it coincides with the solution on the restricted domain in which the second argument is fixed to be the "trivial" one. Under this category we survey mostly solutions in which the structure is a partition of the set of the players, and a solution in which the structure is a graph, the vertices of which are the players.

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This chapter was published in:

  • R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3, 00.
    This item is provided by Elsevier in its series Handbook of Game Theory with Economic Applications with number 3-54.

    Handle: RePEc:eee:gamchp:3-54

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    Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description

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    Cited by:
    1. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M., 2006. "Population Monotonic Path Schemes for Simple Games," Discussion Paper 2006-113, Tilburg University, Center for Economic Research.
    2. Roberto Lucchetti & Paola Radrizzani & Emanuele Munarini, 2011. "A new family of regular semivalues and applications," International Journal of Game Theory, Springer, vol. 40(4), pages 655-675, November.
    3. Ciftci, B.B. & Dimitrov, D.A., 2006. "Stable Coalition Structures in Simple Games with Veto Control," Discussion Paper 2006-114, Tilburg University, Center for Economic Research.
    4. Barbara von Schnurbein, 2010. "The Core of an Extended Tree Game: A New Characterisation," Ruhr Economic Papers 0212, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    5. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.
    6. Jason Barr & Francesco Passarelli, . "Who Has the Power in the EU?," Working Papers Rutgers University, Newark 2004-005, Department of Economics, Rutgers University, Newark.

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