Two Values for Transferable Utility Games with Coalition and Graph Structure
AbstractIn this paper we introduce and characterize two new values for transferable utility games with graph restricted communication and a priori unions. Both values are obtained by applying the Shapley value to an associated TU-game. The graph-partition restricted TU-game is obtained by taking the Myerson graph restricted game and of that the Kamijo partition restricted game. In this game the dividend of any coalition that is neither a subset of a union nor a union of unions is zero. The partition-graph restricted TU-game is obtained by taking the partition restricted game and of that the graph restricted game. In this game the dividend of any coalition that is not connected in the graph is zero. We apply the values to an economic example in which the players in a union represent the cities in a country and the graph represents a network of natural gas pipelines between the cities.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-164/1.
Date of creation: 16 Nov 2011
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cooperative games; coalition structures; graphs; Shapley value;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- van den Brink, Rene & van der Laan, Gerard, 2005.
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- René van den Brink & Gerard van der Laan, 2001. "A Class of Consistent Share Functions for Games in Coalition Structure," Tinbergen Institute Discussion Papers 01-044/1, Tinbergen Institute.
- Brink, J.R. van den & Laan, G. van der, 2001. "A Class of Consistent Share Functions For Games in Coalition Structure," Discussion Paper 2001-33, Tilburg University, Center for Economic Research.
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