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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).

Suggested Citation

  • William Thomson, 2006. "Children crying at birthday parties. Why? Fairness and incentives for cake division problems," RCER Working Papers 526, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:526
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    File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_526.pdf
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    References listed on IDEAS

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    1. Francis Su, "undated". "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
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    3. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 769-783.
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
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    6. 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.
    7. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    8. 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.
    9. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 47-56.
    10. 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.
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    12. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    13. 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.
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    More about this item

    Keywords

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

    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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