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Dividing Goods or Bads Under Additive Utilities

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 147/EC/2016, HSE Working papers from National Research University Higher School of Economics

Abstract: The Competitive Equilibrium with Equal Incomes is an especially appealing ecient 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 ecient frontier. But it is far from resolute, allowing routinely many divisions with sharply di erent welfare consequences. Even the much more permissive No Envy property is profoundly ambiguous in the division of bads: the set of ecient and envy-free allocations can have many connected components, and has no single-valued selection continuous in the marginal rates. The CEEI to divide goods is Resource Monotonic (RM): everyone (weakly) bene ts when the manna increases. But when we divide bads eciently, RM is incompatible with Fair Share Guarantee, a much weaker property than No Envy.

Keywords: fair division of goods; fair division of 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-com, nep-gth, nep-hpe and nep-mic
Date: 2016
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Published in WP BRP Series: Economics / EC, August 2016, pages 1-33

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