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Axiomatizations of Permission Values for Games with a Hierarchical Permission Structure using Split Neutrality

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  • René van den Brink

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

Abstract

Recently, cooperative game theory has been applied to various economic allocation problems in which players are not fully anonymous but belong to some relational structure. One of the most developed models in this respect are communications situations or (symmetric) network situations in which players can only cooperate if there are sufficient communication links in the communication network.Another class of applications considers situations in which the players are hierarchically ordered, i.e. they are part of a structure of asymmetric relations. Examples are auctions, airport games, sequencing situations, the water distribution problem and hierarchically structured firms. This paper is about games with permission structure being a general game theoretic model to study situations with asymmetric relations between the players. We provide new axiomatic characterizations of the Shapley permission values and the first characterizations of the Banzhaf permission values using split properties which say something about the payoffs of players if we split certain players in two.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-100/1.

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Date of creation: 09 Dec 2003
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Handle: RePEc:dgr:uvatin:20030100

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Web page: http://www.tinbergen.nl

Related research

Keywords: Cooperative game theory; hierarchical permission structure; Shapley value; Banzhaf value; split neutrality;

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  1. Ambec, S. & Sprumont, Y., 2000. "Sharing a River," Papers 00-06, Laval - Recherche en Energie.
  2. 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.
  3. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1993. "Cooperation in one machine scheduling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154197, Tilburg University.
  4. Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2002. "Tree-connected peer group situations and peer group games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91321, Tilburg University.
  5. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2001. "Axiomatizations of the Shapley Value for Cooperative Games on Antimatroids," Discussion Paper 2001-99, Tilburg University, Center for Economic Research.
  6. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper 2000-124, Tilburg University, Center for Economic Research.
  7. 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.
  8. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  9. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
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