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Abstract

It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of (weighted) digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only in order to generate worth, but does not need its predecessors in order to give permission to its own successors. We introduce and axiomatize a Shapley value type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the beta-measure for weighted digraphs.

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File URL: http://papers.tinbergen.nl/12126.pdf
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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-126/II.

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Date of creation: 27 Nov 2012
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Handle: RePEc:dgr:uvatin:20120126

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

Related research

Keywords: Cooperative TU-game; peer group game; digraph game; game with a permission structure; local permission structure;

Find related papers by JEL classification:

• C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

This paper has been announced in the following NEP Reports:

• NEP-ALL-2012-12-15 (All new papers)
• NEP-GTH-2012-12-15 (Game Theory)
• NEP-MIC-2012-12-15 (Microeconomics)

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1. 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.
   
   • Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2000. "Tree-connected Peer Group Situations and Peer Group Games," Discussion Paper 2000-117, Tilburg University, Center for Economic Research.
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   • Brink, J.R. van den & Borm, P.E.M., 1994. "Digraph competitions and cooperative games," Discussion Paper 1994-24, Tilburg University, Center for Economic Research.
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   • Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
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7. Derks, Jean & Haller, Hans & Peters, Hans, 2000. "The selectope for cooperative games," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12221, Maastricht University.
   
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10. Algaba, A. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J., 2000. "The position value for union stable systems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-84483, Tilburg University.
    
    • Algaba, E. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J.J., 1998. "The position value for union stable systems," Research Memorandum 768, Tilburg University, Faculty of Economics and Business Administration.
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12. 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.
13. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-39, December.
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