Competitive division of a mixed manna

Bogomolnaia, A. , Moulin, H. , Sandomirskiy, F. and Yanovskaya, E. (2017) Competitive division of a mixed manna. Econometrica, 85(6), pp. 1847-1871. (doi: 10.3982/ECTA14564)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Moulin, Professor Herve and Bogomolnaia, Professor Anna
Authors: Bogomolnaia, A., Moulin, H., Sandomirskiy, F., and Yanovskaya, E.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Econometrica
Publisher:Econometric Society
ISSN (Online):1468-0262
Published Online:04 December 2017
Copyright Holders:Copyright © 2017 The Econometric Society
First Published:First published in Econometrica 85(6): 1847-1871
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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