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Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

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  • Yeon-Koo Che
  • Fuhito Kojima

Abstract

The random priority (random serial dictatorship) mechanism is a common method for assigning objects. The mechanism is easy to implement and strategy-proof. However, this mechanism is inefficient, because all agents may be made better off by another mechanism that increases their chances of obtaining more preferred objects. This form of inefficiency is eliminated by a mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications is an open question. We show 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. Copyright 2010 The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 78 (2010)
Issue (Month): 5 (09)
Pages: 1625-1672

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Handle: RePEc:ecm:emetrp:v:78:y:2010:i:5:p:1625-1672

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Cited by:
  1. Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.
  2. Budish, Eric & Cantillon, Estelle, 2010. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," CEPR Discussion Papers 7641, C.E.P.R. Discussion Papers.
  3. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2012. "Promoting School Competition Through School Choice: A Market Design Approach," Discussion Papers 12-036, Stanford Institute for Economic Policy Research.
  4. Athanassoglou, Stergios, 2011. "Efficiency under a combination of ordinal and cardinal information on preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 180-185, March.
  5. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
  6. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer, vol. 41(1), pages 203-215, June.

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