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Competitive division of a mixed manna

Anna Bogomolnaia (), Herve Moulin (), Fedor Sandomirskiy () and Elena Yanovskaya ()
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Anna Bogomolnaia: National Research University Higher School of Economics
Fedor Sandomirskiy: National Research University Higher School of Economics
Elena Yanovskaya: National Research University Higher School of Economics

No WP BRP 158/EC/2017, HSE Working papers from National Research University Higher School of Economics

Abstract: A mixed manna contains goods (that everyone likes), 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 homothetic, concave (and monotone), the Competitive Equilibrium with Equal Incomes maximizes the Nash product of utilities: hence it is welfarist (determined utility-wise by the feasible set of pro les), single-valued and easy to compute. We generalize the Gale-Eisenberg Theorem to a mixed manna. The Competitive division is still welfarist and related to the product of utilities or disutilities. If the zero utility pro le (before any manna) is Pareto dominated, the competitive pro le is unique and still maximizes the product of utilities. If the zero pro le is unfeasible, the competitive pro les are the critical points of the product of disutilities on the eciency frontier, and multiplicity is pervasive. In particular the task of dividing a mixed manna is either good news for everyone, or bad news for everyone. We re ne our results in the practically important case of linear preferences, where the axiomatic comparison between the division of goods and that of bads is especially sharp. When we divide goods and the manna improves, everyone weakly bene ts under the competitive rule; but no reasonable rule to divide bads can be similarly Resource Monotonic. Also, the much larger set of Non Envious and Ecient divisions of bads can be disconnected so that it will admit no continuous selection.

Keywords: fair division; mixed manna; goods; bads; competitive equilibrium with equal incomes; Nash product; envy-freeness; resource monotonicity; independence of lost bids (search for similar items in EconPapers)
JEL-codes: D61 D63 D82 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-upt
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
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Published in WP BRP Series: Economics / EC, February 2017, pages 1-39

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