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Competitive division of a mixed manna
Высшая школа экономики
,
2017.
No. 158.
Bogomolnaia A., Sandomirskiy F., Moulin H., Elena Yanovskaya
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 profiles), 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 profile (before any manna) is Pareto dominated, the competitive profile is unique and still maximizes the product of utilities. If the zero profile is unfeasible, the competitive profiles are the critical points of the product of disutilities on the efficiency 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 refine 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 benefits 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 Efficient divisions of bads can be disconnected so that it will admit no continuous selection.
Language:
English
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / Высшая школа экономики. Series EC "Economics". 2016. No. 147.
The Competitive Equilibrium with Equal Incomes is an especially appealing efficient and envy-free division of private goods when utilities are additive: it maximizes the Nash product of utilities and is single-valued and continuous in the marginal rates of substitution. The CEEI to divide bads captures similarly the critical points of the Nash product in the ...
Added: August 19, 2016
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / Cornell university, arXiv.org. Series arXiv:1608.01540 "Computer Science". 2016.
The Competitive Equilibrium with Equal Incomes is an especially appealing efficient and envy-free division of private goods when utilities are additive: it maximizes the Nash product of utilities and is single-valued and continuous in the marginal rates of substitution. The CEEI to divide bads captures similarly the critical points of the Nash product in the ...
Added: October 14, 2016
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., Econometrica 2017 Vol. 85 No. 6 P. 1847-1871
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 ...
Added: October 14, 2016
Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / Высшая школа экономики. Series EC "Economics". 2016. No. 153.
When utilities are additive, we uncovered in our previous paper (Dividing Goods or Bads Under Additive Utilities) many similarities but also surprising dierences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the product of utilities ...
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Bogomolnaia A., Moulin H., Sandomirskiy F. et al., / Cornell university, arXiv.org. Series arXiv:1610.03745 [cs.GT] "Computer Science". 2016.
When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the ...
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