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Children crying at birthday parties. Why? Fairness and incentives for cake division problems

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Abstract

We consider the problem of dividing a non-homogeneous one- dimensional continuum whose endpoints are topologically identi¯ed. Examples are the division of a birthday cake, the partition of a circular market, the assignment of sentry duty or medical call. We study the existence of rules satisfying various requirements of fairness (no-envy, egalitarian-equivalence; and several requirements having to do with changes in the data of the problem), and that induce agents to reveal their preferences honestly (strategy-proofness).

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_526.pdf
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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 526.

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Length: 34 pages
Date of creation: Apr 2006
Date of revision:
Handle: RePEc:roc:rocher:526

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: cake division; no-envy; strategy-proofness.;

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  1. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
  2. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  3. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Moulin, Herve, 1987. "The Pure Compensation Problem: Egalitarianism versus Laissez-Fairism," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 769-83, November.
  6. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Barbanel, Julius B. & Brams, Steven J., 2004. "Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 251-269, November.
  8. Maniquet, F., 2000. "A Characterization of the Shapley Value in Queueing Problems," Papers 222, Notre-Dame de la Paix, Sciences Economiques et Sociales.
  9. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  10. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56.
  11. H. R. Varian, 1973. "Equity, Envy and Efficiency," Working papers 115, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Jeroen Suijs, 1996. "On incentive compatibility and budget balancedness in public decision making," Review of Economic Design, Springer, vol. 2(1), pages 193-209, December.
  13. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
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