Economic Theory

, Volume 50, Issue 2, pp 463–488 | Cite as

The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods

  • Onur Kesten
  • Ayşe YazıcıEmail author
Research Article


We study the problem of allocating a set of indivisible goods among a set of agents when monetary transfers are not allowed. We consider two interesting cases of this problem: (1) the supply of each object is exactly one; and (2) the supply of an object may be greater than one. Our central requirements are strategy-proofness and ex post fairness. We propose a particular rule satisfying strategy-proofness and no-envy (as well as equal treatment of equals). For the first case, it Pareto dominates any other rule satisfying strategy-proofness and equal treatment of equals. For the second case, it Pareto dominates any other rule satisfying strategy-proofness and no-envy.


Indivisible goods Strategy-proofness Fairness No-envy 

JEL Classification

C71 C78 D71 D78 


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  1. Abdulkadiroğlu A., Sönmez T.: House allocation with existing tenants. J Econ Theory 88, 233–260 (1999)CrossRefGoogle Scholar
  2. Abdulkadiroğlu A., Sönmez T.: School choice: A mechanism design approach. Am Econ Rev 93, 729–747 (2003)CrossRefGoogle Scholar
  3. Alkan A., Demange G., Gale D.: Fair allocation of indivisible goods and criteria of justice. Econometrica 59, 1023–1039 (1991)CrossRefGoogle Scholar
  4. Biró, P.: Student admissions in Hungary as Gale and Shapley Envisaged. University of Glasgow Technical Report TR-2008-291 (2008)Google Scholar
  5. Bogomolnaia A., Moulin H.: A new solution to the random assignment problem. J Econ Theory 100, 295–328 (2001)CrossRefGoogle Scholar
  6. Bogomolnaia A., Moulin H.: A simple random assignment problem with a unique solution. Econ Theory 19, 623–636 (2002)CrossRefGoogle Scholar
  7. Brams, S., Taylor, A.: Fair Division: from Cake-Cutting to Dispute Resolution: New York: Cambridge University Press (1996)Google Scholar
  8. Brams S., King D.L.: Efficient fair division: Help the worst off or avoid envy?. Ration Soc 17, 387–421 (2005)CrossRefGoogle Scholar
  9. Budish, E., Cantillon, E.: The multi-unit assignment problem: theory and evidence from course allocation at Harvard. Working paper, Harvard University (2009)Google Scholar
  10. Che, Y.-K., Kojima, F.: Asymptotic equivalence of random priority and probabilistic serial rules. Econometrica (2010)Google Scholar
  11. Ehlers L.: Coalitional strategy-proof house allocation. J Econ Theory 105, 298–317 (2002)CrossRefGoogle Scholar
  12. Ehlers L., Klaus B.: Efficient priority rules. Games Econ Behav 55, 372–384 (2006)CrossRefGoogle Scholar
  13. Ergin H.: Efficient resource allocation on the basis of priorities. Econometrica 70, 2489–2497 (2002)CrossRefGoogle Scholar
  14. Fleurbaey M., Maniquet F.: Implementability and horizontal fairness require no-envy. Econometrica 65, 1215–1219 (1997)CrossRefGoogle Scholar
  15. Foley D.: Resource allocation and public sector. Yale Economic Essays 7, 45–98 (1967)Google Scholar
  16. Gale D., Shapley L.S.: College admissions and the stability of marriage. Am Math Mon 69, 9–15 (1962)CrossRefGoogle Scholar
  17. Hylland A., Zeckhauser R.: The efficient allocation of individuals to positions. J Polit Econ 87, 293–314 (1979)CrossRefGoogle Scholar
  18. Kesten O.: On two competing rules for priority based allocation problems. J Econ Theory 127, 155–171 (2006)CrossRefGoogle Scholar
  19. Kesten O.: Why do popular mechanisms lack efficiency in random environments. J Econ Theory 144, 2209–2226 (2009)CrossRefGoogle Scholar
  20. Klaus B., Miyagawa E.: Strategy-proofness, solidarity, and consistency for multiple assignment problems. Int J Game Theory 30, 421–435 (2002)CrossRefGoogle Scholar
  21. Klijn F.: An algorithm for envy-free allocations in an economy with indivisible objects and money. Soc Choice Welfare 17, 201–216 (2000)CrossRefGoogle Scholar
  22. Kojima, F., Manea, M.: Axioms for deferred acceptance. Econometrica (2010)Google Scholar
  23. Ma J.: On Randomized Matching Mechanisms. Econ Theory 8, 377–381 (1996)Google Scholar
  24. Pápai S.: Strategy-proof assignment by hierarchical exchange. Econometrica 68, 1403–1433 (2000a)CrossRefGoogle Scholar
  25. Pápai S.: Strategy-proof multiple assignment using quotas. Rev Econ Design 5, 91–105 (2000b)CrossRefGoogle Scholar
  26. Pápai S.: Strategy-proof single unit award rules. Soc Choice Welfare 18, 785–798 (2001a)CrossRefGoogle Scholar
  27. Pápai S.: Strategy-proof and nonbossy multiple assignments. J Public Econ Theory 3, 257–271 (2001b)CrossRefGoogle Scholar
  28. Roth, A., Sotomayor, M.: Two-sided Matching: New York: Cambridge University Press (1990)Google Scholar
  29. Roth A., Vande Vate J.H.: Incentives in two-sided matching with random stable mechanisms. Econ Theory 1, 31–44 (1991)CrossRefGoogle Scholar
  30. Shapley L., Scarf H.: On cores and indivisibility. J Math Econ 1, 23–28 (1974)CrossRefGoogle Scholar
  31. Svensson L.-G.: Large indivisibles: an analysis with respect to price equilibrium and fairness. Econometrica 51, 939–954 (1983)CrossRefGoogle Scholar
  32. Svensson L.-G.: Strategy-proof allocation of indivisible goods. Soc Choice Welfare 16, 323–330 (1999)CrossRefGoogle Scholar
  33. Tadenuma K., Thomson W.: The fair allocation of an indivisible good when monetary compensations are possible. Math Soc Sci 25, 117–132 (1993)CrossRefGoogle Scholar
  34. Takamiya K.: Coalition strategy-proofness and monotonicty in Shapley-Scarf housing markets. Math Soc Sci 41, 201–213 (2001)CrossRefGoogle Scholar
  35. Thomson, W.: The theory of fair allocation. Book manuscript (2000)Google Scholar
  36. Zhou L.: On a conjecture by Gale about one sided matching problems. J Econ Theory 52, 120–135 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of EconomicsUniversity of RochesterRochesterUSA

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