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Axiomatizations of two types of Shapley values for games on union closed systems

  • René Brink

    ()

  • Ilya Katsev

    ()

  • Gerard Laan

    ()

This discussion paper led to a publication in 'Economic Theory' , 47(1), 175-88. A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson rule for conference structures.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 47 (2011)
Issue (Month): 1 (May)
Pages: 175-188

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Handle: RePEc:spr:joecth:v:47:y:2011:i:1:p:175-188
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  1. Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "The Shapley value for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/56, Centro de Estudios Andaluces.
  2. Youngsub Chun, 2006. "No-envy in queueing problems," Economic Theory, Springer, vol. 29(1), pages 151-162, September.
  3. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
  4. E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2003. "Axiomatizations of the Shapley value for cooperative games on antimatroids," Mathematical Methods of Operations Research, Springer, vol. 57(1), pages 49-65, 04.
  5. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
  6. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, vol. 33(2), pages 349-364, November.
  7. Yair Tauman & Naoki Watanabe, 2007. "The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results," Economic Theory, Springer, vol. 30(1), pages 135-149, January.
  8. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
  9. van den Brink, J.R. & Gilles, R.P., 1991. "Axiomatizations of the conjunctive permission value for games with permission structures," Research Memorandum FEW 485, Tilburg University, School of Economics and Management.
  10. repec:spr:compst:v:57:y:2003:i:1:p:49-65 is not listed on IDEAS
  11. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
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