 Competitive Division of a Mixed MannaAnna Bogomolnaia, Herve Moulin, Fedor Sandomirskiy and Elena Yanovskaya Econometrica, 2017, vol. 85, issue 6, 1847-1871 Abstract: A mixed manna contains goods (that everyone likes) and bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale–Eisenberg): hence it is welfarist (determined by the set of feasible utility profiles), unique, continuous, and easy to compute. We show that the competitive division of a mixed manna is still welfarist. If the zero utility profile is Pareto dominated, the competitive profile is strictly positive and still uniquely maximizes the product of utilities. If the zero profile is unfeasible (for instance, if all items are bads), the competitive profiles are strictly negative and are the critical points of the product of disutilities on the efficiency frontier. The latter allows for multiple competitive utility profiles, from which no single‐valued selection can be continuous or resource monotonic. Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods. Date: 2017 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wly:emetrp:v:85:y:2017:i:6:p:1847-1871 Ordering information: This journal article can be ordered from Access Statistics for this article Econometrica is currently edited by Guido W. Imbens More articles in Econometrica from Econometric Society Contact information at EDIRC. |
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