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Dividing Goods or Bads Under Additive Utilities

Author

Listed:
  • Anna Bogomolnaia

    () (National Research University Higher School of Economics)

  • Herve Moulin

    () (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)

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.

Suggested Citation

  • Anna Bogomolnaia & Herve Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2016. "Dividing Goods or Bads Under Additive Utilities," HSE Working papers WP BRP 147/EC/2016, National Research University Higher School of Economics.
  • Handle: RePEc:hig:wpaper:147/ec/2016
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    File URL: https://www.hse.ru/data/2016/08/19/1118748210/147EC2016.pdf
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    References listed on IDEAS

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    1. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
    2. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    3. Balazs Sziklai & Erel Segal-Halevi, 2015. "Resource-monotonicity and Population-monotonicity in Cake-cutting," IEHAS Discussion Papers 1552, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    4. Nagahisa, Ryo-ichi, 1991. "A local independence condition for characterization of Walrasian allocations rule," Journal of Economic Theory, Elsevier, vol. 54(1), pages 106-123, June.
    5. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, Oxford University Press, vol. 92(4), pages 671-687.
    6. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
    7. Moulin, Herve, 1990. "Uniform externalities : Two axioms for fair allocation," Journal of Public Economics, Elsevier, vol. 43(3), pages 305-326, December.
    8. Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    9. van den Nouweland, A. & Peleg, B. & Tijs, S., 1996. "Axiomatic characterizations of the Walras correspondence for generalized economies," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 355-372.
    10. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    11. Moulin, Herve, 1991. "Welfare bounds in the fair division problem," Journal of Economic Theory, Elsevier, vol. 54(2), pages 321-337, August.
    12. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    13. John Winsor Pratt & Richard Jay Zeckhauser, 1990. "The Fair and Efficient Division of the Winsor Family Silver," Management Science, INFORMS, vol. 36(11), pages 1293-1301, November.
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    Cited by:

    1. Misha Gavrilovich & Victoria Kreps, 2016. "Games with Incomplete Information on One Side as Games with Incomplete Information on Both Sides and Asymmetric Computational Resources," HSE Working papers WP BRP 154/EC/2016, National Research University Higher School of Economics.
    2. Anna Bogomolnaia & Herve Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2016. "Dividing Goods and Bads Under Additive Utilities," HSE Working papers WP BRP 153/EC/2016, National Research University Higher School of Economics.

    More about this item

    Keywords

    fair division of goods; fair division of bads; competitive equilibrium with equal incomes; Nash product; envy-freeness; resource monotonicity; independence of lost bids.;

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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