IJPAM: Volume 75, No. 3 (2012)

ON THE INVERSE PROBLEM FOR MULTIWEIGHTED
SHAPLEY VALUES OF COOPERATIVE TU GAMES

Irinel Dragan
Department of Mathematics
University of Texas at Arlington
Arlington, TX 76019, USA


Abstract. In this paper, we solve the inverse problem for the class of Values of Cooperative TU games, called the Multiweighted Shapley Values, introduced in an earlier work of the author (see [#!Dr:multi!#]): find out the set of games for which the MWSV equals an apriori given n-vector. The inverse problem for other values has been solved in previous works ([#!Dr:pot!#] and [#!Dr:invsemi!#]), but the approach is different here.

Received: July 27, 2011

AMS Subject Classification: 91A12

Key Words and Phrases: the Shapley Value, the Multiweighted Shapley Value, the inverse problem, the null space of a linear operator

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 3