Journal of Mathematics and Statistics

Two Main Methods for Utility Sharing in Joint Business: A Discussion

Rafel Amer, Francesc Carreras and Antonio Magaña

DOI : 10.3844/jmssp.2007.28.34

Journal of Mathematics and Statistics

Volume 3, Issue 1

Pages 28-34


One of the main purposes of any theory of joint business is to provide a convincing way for sharing the total utility available to the set of agents. The proportional rule is widely applied in practice but people using this method should be warned that it is not as innocent, effective, fair and consistent as it seems at first glance. Indeed, restricted domain, low sensibility derived from ignoring most marginal contributions, unjustified double discriminatory level and lack of additivity that derives in serious inconsistencies in costs/savings and added costs problems form part of the negative baggage of this rule, a fact that will probably surprise theorists and practitioners. Instead, nothing of this concerns the Shapley value whence the main conclusion of our analysis, which we hope the readers will find of interest, is that the Shapley value should replace the proportional rule in cooperative affairs and pure bargaining problems.


© 2007 Rafel Amer, Francesc Carreras and Antonio Magaña. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.