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

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Author Info
RenÊ van den Brink (Department of Econometrics, Free University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

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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.

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Publisher Info
Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 26 (1997)
Issue (Month): 1 ()
Pages: 27-43
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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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  1. Brink, R. van den, 1999. "An axiomatization of the shapley value using a fairness property," Discussion Paper 120, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure," Tinbergen Institute Discussion Papers 08-104/1, Tinbergen Institute. [Downloadable!]
  3. Brink, R. van den & Ruys, P.H.M., 2005. "Technological change, wages and firm size," Discussion Paper 22, Tilburg University, Tilburg Law and Economic Center. [Downloadable!]
  4. René van den Brink, 2003. "Axiomatizations of Permission Values for Games with a Hierarchical Permission Structure using Split Neutrality," Tinbergen Institute Discussion Papers 03-100/1, Tinbergen Institute. [Downloadable!]
  5. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers 06-114/1, Tinbergen Institute. [Downloadable!]
  6. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2003. "Harsanyi Solutions in Line-graph Games," Tinbergen Institute Discussion Papers 03-076/1, Tinbergen Institute. [Downloadable!]
  7. Brink, Rene van den & Gilles, Robert P., 2005. "Explicit and latent authority in hierarchical organizations," Discussion Paper 75, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  8. Gilles, R.P. & Owen, G., 1999. "Cooperative games and disjunctive permission structures," Discussion Paper 20, Tilburg University, Center for Economic Research. [Downloadable!]
  9. René van den Brink, 2006. "On Hierarchies and Communication," Tinbergen Institute Discussion Papers 06-056/1, Tinbergen Institute. [Downloadable!]
  10. Ruys, P.H.M., 2002. "A managed service economy with an equilibrium for marketable services," Discussion Paper 1, Tilburg University, Center for Economic Research. [Downloadable!]
  11. Algaba, E. & Bilbao, J.M. & Brink, R. van den, 2000. "Cooperative games on antimatroids," Discussion Paper 124, Tilburg University, Center for Economic Research. [Downloadable!]
  12. Algaba, E. & Bilbao, J.M. & Brink, R. van den & Jimenez-Losada, A., 2001. "Axiomatizations of the shapley value for cooperative games on antimatroids," Discussion Paper 99, Tilburg University, Center for Economic Research. [Downloadable!]
  13. René van den Brink & Frank Steffen, 2008. "Axiomatizations of a Positional Power Score and Measure for Hierarchies," Tinbergen Institute Discussion Papers 08-115/1, Tinbergen Institute. [Downloadable!]
  14. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute. [Downloadable!]
  15. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute. [Downloadable!]
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