The Core of an Extended Tree Game: A New Characterisation
AbstractCost allocation problems on networks can be interpreted as cooperative games on a graph structure. In the classical standard tree game, the cost of a service delivered, by a source has to be allocated between homogeneous users at the vertices. But, modern networks have also the capacity to supply different (levels of) services. For example, a cable network that provides diff erent television standards. Users that choose different levels of service can not be treated equally. The extended tree game accounts for such differences between users. Here, players are characterised by their level of demand, consequently the implications on the cost structure of the problem can be considered. We show how an ET-game can be formulated as the sum of unanimity games. This observation enables us to directly calculate the weighted Shapley values and to identify the core of an ET-game.
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Bibliographic InfoPaper provided by Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen in its series Ruhr Economic Papers with number 0212.
Length: 22 pages
Date of creation: Nov 2010
Date of revision:
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
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