A Weighted Pseudo-potential Approach to Values for TU-games

Driessen, Theo S.H. and Radzik, Tadeusz (2002) A Weighted Pseudo-potential Approach to Values for TU-games. International Transactions in Operational Research, 9 (3). pp. 303-320. ISSN 0969-6016

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Abstract:	This paper provides a twofold generalization of the well-known characterization of the Shapley value for TU-games as the discrete gradient of a so-called potential function. On the one hand the potential approach is extended to the so-called weighted pseudo-potential approach in the sense that the extended representation may incorporate, besides a fraction of the discrete gradient, a fraction of the underlying pseudo-potential function itself, as well as a fraction of the average of all the components of the gradient. On the other hand the paper fully characterizes the class of values for TU-games that admit a weighted pseudo-potential representation. Besides two individual constraints, these values have to be efficient, symmetric, and linear. The theory developed is illustrated by several examples of such values and their weighted pseudo-potential representations are discussed.
Item Type:	Article
Copyright:	© 2002 Wiley InterScience
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/71566
Official URL:	http://dx.doi.org/10.1111/1475-3995.00357
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