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

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Author Info
William Thomson () (University of Rochester)

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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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Publisher 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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Related research
Keywords: cake division no-envy strategy-proofness.

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Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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  1. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges. [Downloadable!]
  2. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Blackwell Publishing, vol. 48(4), pages 587-97, October. [Downloadable!] (restricted)
  3. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56. [Downloadable!] (restricted)
  6. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation, Yale University. [Downloadable!]
  7. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March. [Downloadable!] (restricted)
    Other versions:
  8. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November. [Downloadable!] (restricted)
    Other versions:
  9. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
    Other versions:
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February. [Downloadable!] (restricted)
  13. Brams, Steven J., 1994. "Voting procedures," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 30, pages 1055-1089 Elsevier. [Downloadable!] (restricted)
    Other versions:
    • Brams, Steven J. & Fishburn, Peter, 1998. "Voting Procedures," Working Papers 98-30, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    • Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," 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 1, chapter 4, pages 173-236 Elsevier. [Downloadable!] (restricted)
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