A note on quasi-additive games

• Autores: Francesc Carreras Escobar
• Localización: XXXI Congreso Nacional de Estadística e Investigación Operativa ; V Jornadas de Estadística Pública: Murcia, 10-13 de febrero de 2009 : Libro de Actas, 2009, ISBN 978-84-691-8159-1
• Idioma: inglés
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• Resumen

  • The proportional rule has a long tradition as a sharing method. The natural framework for the proportional rule seems to be the context of pure bargaining problems (PBPs), where only the individual utilities and the utility of the grand coalition are given.

    The Shapley value is not directly applicable to PBPs. We then introduce the idea of closure of a PBP, which leads to quasi-additive games and to de ne a natural Shapley rule for PBPs. Axiomatic characterizations of this sharing rule are given, not only on the full space of PBPS but also on interesting subsets. Among the axioms used, the proportional rule fails to satisfy additivity only. Although this property might seem a \mathematical delicatessen", the curious fact is that the lack of additivity provokes serious inconsistencies of the proportional rule when dealing, for example, with cost-saving related problems or added costs problems. Instead, no inconsistency arises for the Shapley rule.