Potential, value, and coalition formation

  1. Annick Laruelle 1
  2. Federico Valenciano 2
  1. 1 Université de Caen Basse Normandie, Francia
  2. 2 Universidad del País Vasco, España
Journal:
Top

ISSN: 1863-8279 1134-5764

Year of publication: 2008

Volume: 16

Issue: 1

Pages: 73-89

Type: Article

More publications in: Top

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.’