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Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

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Author Info
Yeon-Koo Che () (Columbia University - Department of Economics)
Fuhito Kojima () (Cowles Foundation, Yale University)

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Abstract

The random priority (random serial dictatorship) mechanism is a common method for assigning objects to individuals. The mechanism is easy to implement and strategy-proof. However this mechanism is inefficient, as the agents may be made all better off by another mechanism that increases their chances of obtaining more preferred objects. Such an ineciency is eliminated by the recent mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications has been an open question. This paper shows that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0809-06.

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Date of creation: 2008
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Handle: RePEc:clu:wpaper:0809-06

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  5. Martin W. Cripps & Jeroen M. Swinkels, 2006. "Efficiency of Large Double Auctions," Econometrica, Econometric Society, vol. 74(1), pages 47-92, 01. [Downloadable!] (restricted)
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  6. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January. [Downloadable!] (restricted)
  7. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April. [Downloadable!] (restricted)
  8. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August. [Downloadable!] (restricted)
  9. Jackson, Matthew O. & Manelli, Alejandro M., 1997. "Approximately Competitive Equilibria in Large Finite Economies," Journal of Economic Theory, Elsevier, vol. 77(2), pages 354-376, December. [Downloadable!] (restricted)
  10. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September. [Downloadable!] (restricted)
  11. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2008. "Expanding "Choice" in School Choice," Discussion Papers 0809-09, Columbia University, Department of Economics. [Downloadable!]
  12. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October. [Downloadable!] (restricted)
  13. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January. [Downloadable!] (restricted)
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