Potential,value, and coalition formation |
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Authors: | Annick Laruelle Federico Valenciano |
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Institution: | (1) Faculté des Sciences Economiques et de Gestion, Université de Caen Basse Normandie, Esplanade de la Paix, 14000 Caen, France;(2) Departamento de Economía Aplicada IV, Universidad del País Vasco, Avenida Lehendakari Aguirre, 83, 48015 Bilbao, Spain |
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Abstract: | In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions
of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself
appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s
seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural
relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest
that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion
of ‘value.’
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Keywords: | Coalitional games Value Potential Probabilistic models |
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