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How to cut a pizza fairly: Fair division with decreasing marginal evaluations

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  • Fabio Maccheroni
  • Fabio Maccheroni
  • Massimo Marinacci
  • Massimo Marinacci

Abstract

Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of nonatomic probability measures, we extend some of these results to the case of individuals with decreasing marginal evaluations. Copyright Springer-Verlag Berlin Heidelberg 2003

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 20 (2003)
Issue (Month): 3 (06)
Pages: 457-465

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Handle: RePEc:spr:sochwe:v:20:y:2003:i:3:p:457-465

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References

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  1. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
  2. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  3. Alain Chateauneuf & Fabio Macheronni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00177057, HAL.
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  5. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June.
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Citations

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Cited by:
  1. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
  2. Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
  3. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Economics Papers from University Paris Dauphine 123456789/6223, Paris Dauphine University.
  4. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
  5. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Department of Economics, Bar-Ilan University.
  6. Nobusumi Sagara & Milan Vlach, 2011. "A new class of convex games on σ-algebras and the optimal partitioning of measurable spaces," International Journal of Game Theory, Springer, vol. 40(3), pages 617-630, August.
  7. Marco Dall'Aglio & Fabio Maccheroni, 2007. "Disputed Lands," Carlo Alberto Notebooks 58, Collegio Carlo Alberto.
  8. Marco LiCalzi & Antonio Nicolò, 2005. "Efficient Egalitarian Equivalent Allocations over a Single Good," Microeconomics 0510014, EconWPA.
  9. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506 Elsevier.
  10. Thibault Gadjos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," Working Papers 2002-33, Centre de Recherche en Economie et Statistique.
  11. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.

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