Monotonicity properties of bargaining solutions when applied to economics |
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| Affiliation: | 1. The Center for Host Defense, Inflammation, and Lung Disease (CHILD) Research, Department of Pediatrics, The Pennsylvania State University College of Medicine, Hershey, PA, USA;2. Department of Obstetrics and Gynecology, The Pennsylvania State University College of Medicine, Hershey, PA, USA;1. The Department of Pediatric Surgery, Rigshospitalet, DK-2100 Copenhagen;2. Section of Endocrinology, Department of Pediatrics, Hvidovre University Hospital, Copenhagen;3. Faculty of Health Science, University of Copenhagen;4. Department of Pathology, Rigshospitalet, Copenhagen;5. Douglas Stephens Surgical Research Laboratory, Murdoch Childrens Research Institute, Melbourne, Australia;6. Department of Paediatric Urology, Royal Children’s Hospital, Melbourne, Australia;7. Department of Paediatrics, University of Melbourne |
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| Abstract: | We are concerned with the application of bargaining solutions to economic problems of fair division, and, in particular, with the way they respond to changes in the amount to be divided. For instance, one may want an increase in that amount to benefit all agents. A variety of monotonicity properties have been studied in the abstract framework of bargaining theory. Most of the commonly studied solutions are known not to satisfy many of these properties. Here, we investigate the extent to which they do when applied to economics. We show that when there is only one good, they do in fact satisfy many monotonicity properties that they do not satisfy in general. However, this positive result fails as soon as the number of commodities is greater than 2. |
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