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An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure

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  • RenÊ van den Brink

    (Department of Econometrics, Free University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

Abstract

Players that participate in a cooperative game with transferable utilities are assumed to be part of a permission structure being a hierarchical organization in which there are players that need permission from other players before they can cooperate. Thus a permission structure limits the possibilities of coalition formation. Various assumptions can be made about how a permission structure affects the cooperation possibilities. In this paper we consider the disjunctive approach in which it is assumed that each player needs permission from at least one of his predecessors before he can act. We provide an axiomatic characterization of the disjunctive permission value being the Shapley value of a modified game in which we take account of the limited cooperation possibilities.

Suggested Citation

  • RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 27-43.
  • Handle: RePEc:spr:jogath:v:26:y:1997:i:1:p:27-43
    Note: Received May 1994 Revised version January 1995
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    Cited by:

    1. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    2. René Brink & Pieter Ruys, 2008. "Technology driven organizational structure of the firm," Annals of Finance, Springer, vol. 4(4), pages 481-503, October.
    3. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    4. René Brink & Ilya Katsev & Gerard Laan, 2011. "A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 591-616, August.
    5. Lei Li & Xueliang Li, 2011. "The covering values for acyclic digraph games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 697-718, November.

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