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On the Computation of Weighted Shapley Values for Cooperative TU Games

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On the Computation of Weighted Shapley Values for Cooperative TU Games

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Title: On the Computation of Weighted Shapley Values for Cooperative TU Games
Author: Dragan, Irinel C.
Abstract: This paper is considering the problem of dividing fairly the worth of the grand coalition in a transferable utilities game, in case that the coalition is formed. The computational experience for the Shapley Value, the most famous solution, is extensive, but the case of the Weighted Shapley Value and that of the Kalai-Samet Value have been barely considered. Based upon some results connected to the null space of the first of these last two operators, an algorithm for computing the Weighted Shapley Value is developed. The case of the Kalai-Samet Value, a more general value, that is reducible to a vector of weighted values, is also considered. A nice new algorithm to be used for the particular case of the Shapley Value, is derived from the Weighted Shapley Value algorithm. Examples are illustrating the stated algorithms applied to all cases.
URI: http://hdl.handle.net/10106/2338
Date: 2008

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