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.
Original language | Undefined |
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Pages (from-to) | 303-320 |
Number of pages | 19 |
Journal | International transactions in operational research |
Volume | 9 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2002 |
Keywords
- Cooperative TU game
- Value
- IR-71566
- weighted pseudo-potential
- METIS-208496
- weighted pseudo-gradient