Economic Theory

, Volume 31, Issue 3, pp 501–521

Children Crying at Birthday Parties. Why?

Research Article

Abstract

We consider the problem of dividing a non-homogeneous one-dimensional continuum whose endpoints are topologically identified. 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 requirements of efficiency, fairness (no-envy), and immunity to misrepresentation of preferences (strategy-proofness).

Keywords

Cake division No-envy Strategy-proofness 

JEL Classification Numbers

D63 D70 

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References

  1. Barbanel J. (2005) The geometry of efficient fair division. Cambridge University Press, CambridgeGoogle Scholar
  2. Barbanel J., Brams S. (2004) Cake-division with minimal cuts: envy-free procedures for three persons, four persons, and beyond. Math Soc Sci 48, 251–270CrossRefGoogle Scholar
  3. Barbanel, J., Brams, S. Cutting a pie is not a piece of cake. Mimeo 2005Google Scholar
  4. Berliant M., Dunz K., Thomson W. (1992) On the fair division of a heterogeneous commodity. J Math Econ 21, 201–216CrossRefGoogle Scholar
  5. Brams, S., Jones, M., Klamler, C. Perfect cake-cutting procedures with money. Mimeo 2003Google Scholar
  6. Brams S., Taylor A. (1996). Fair division: from cake-cutting to dispute resolution. Cambridge University Press, CambridgeGoogle Scholar
  7. Chun, Y. No-envy in queueing problems. Mimeo 2004Google Scholar
  8. Foley D. (1967) Resource allocation and the public sector. Yale Econo Essays 7, 45–98Google Scholar
  9. Gibbard A. (1973) Manipulation of voting schemes. Econometrica 41, 587–601CrossRefGoogle Scholar
  10. Hill T. (1983) Determining a fair border. Am Math Mon 90, 438–442CrossRefGoogle Scholar
  11. Hurwicz, L. On the interaction between information and incentives in organizations. In: Krippendorff, K. (ed.) Communication and Control in Society pp. 123–147. NY: Scientific Publishers Inc. 1978Google Scholar
  12. Kolm S. (1988) Justice et Equité. Paris: Editions du Centre National de la Recherche Scientifique, 1972. English Edition, MIT Press, CambridgeGoogle Scholar
  13. Maniquet F. (2003) A characterization of the Shapley value in queueing problems. J Econ Theory 109, 90–103CrossRefGoogle Scholar
  14. Maskin E. (1999) Nash equilibrium and welfare optimality. Rev Econo Stud 66, 83–114CrossRefGoogle Scholar
  15. Moulin H. (1987) The pure compensation problem: egalitarianism versus laissez-fairism. Q J Econ 101, 769–783CrossRefGoogle Scholar
  16. Moulin, H. On scheduling fees to prevent merging, splitting and transferring of jobs. Mimeo 2004Google Scholar
  17. Pazner E., Schmeidler D. (1978) Egalitarian equivalent allocations: A, new concept of economic equity. Q J Econ 92, 671–687CrossRefGoogle Scholar
  18. Robertson J., Webb W. (1998) Cake-cutting algorithms. AK Peters, NatickGoogle Scholar
  19. Satterthwaite M. (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorem for voting procedures and social choice functions. J Econ Theory 10, 187–217CrossRefGoogle Scholar
  20. Satterthwaite M., Sonnenschein H. (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48, 587–597CrossRefGoogle Scholar
  21. Schummer J. (1997) Strategy-proofness versus efficiency on restricted domains of exchange economies. Soc Choice Welfare 14, 47–56CrossRefGoogle Scholar
  22. Steinhaus H. (1948) The problem of fair division. Econometrica 16, 101–104Google Scholar
  23. Stromquist N. (1980) How to cut a cake fairly. Am Math Mon 87, 640–644CrossRefGoogle Scholar
  24. Su F. (1999) Rental harmony: Sperner’s lemma in fair division. Am Math Mon 106, 930–942CrossRefGoogle Scholar
  25. Suijs J. (1996) On incentive compatibility and budget balancedness in public decision making. Econ Design 2, 193–209CrossRefGoogle Scholar
  26. Thomson W. (1983) The fair division of a fixed supply among a growing population. Math Oper Res 8, 19–326CrossRefGoogle Scholar
  27. Thomson W. (1987). The vulnerability to manipulative behavior of economic mechanisms designed to select equitable and efficient outcomes. In: Groves T, Radner R., Reiter S. (eds). chap 14, pp 375–396. information, incentives and economic mechanisms. University of Minnesota Press, MinneapolisGoogle Scholar
  28. Thomson W. (1995). Population-monotonic allocation rules. In: Barnett W.A., Moulin H., Salles M., Schofield N. (eds). Social choice, welfare and ethics. Cambridge University Press, cambridgeGoogle Scholar
  29. Thomson W. (1999) Welfare-domination and preference-replacement: a survey and open questions. Soc Choice Welfare 16, 373–394CrossRefGoogle Scholar
  30. Thomson, W. The fair division of time. Mimeo 2003Google Scholar
  31. Varian H. (1974) Equity, envy, and efficiency. J Econ Theory 9, 63–91CrossRefGoogle Scholar
  32. Weller D. (1985) Fair division of measurable space. J Math Econ 14, 5–17CrossRefGoogle Scholar
  33. Zhou L. (1991) Inefficiency of strategy-proof allocation mechanisms in pure exchange economies. Soc Choice Welfare 8, 247–254CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of RochesterRochesterUSA

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