Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

Authors

  • Yeon-Koo Che,

    1. Dept. of Economics, Columbia University, 420 West 118th Street, 1016 IAB, New York, NY 10027, U.S.A. and YERI, Yonsei University, Seoul, Korea; yeonkooche@gmail.com
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  • Fuhito Kojima

    1. Dept. of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, U.S.A; fuhitokojima1979@gmail.com
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    • We are grateful to Susan Athey, Anna Bogomolnaia, Eric Budish, Eduardo Faingold, Dino Gerardi, Johannes Hörner, Mihai Manea, Andy McLennan, Hervé Moulin, Muriel Niederle, Michael Ostrovsky, Parag Pathak, Ben Polak, Al Roth, Kareen Rozen, Larry Samuelson, Michael Schwarz, Tayfun Sönmez, Yuki Takagi, Utku Ünver, Rakesh Vohra and seminar participants at Boston College, Chinese University of Hong Kong, Edinburgh, Harvard, Keio, Kobe, Maryland, Melbourne, Michigan, NYU, Penn State, Queensland, Rice, Rochester, Tokyo, Toronto, Yale, Western Ontario, VCASI, Korean Econometric Society Meeting, Fall 2008 Midwest Meetings, and SITE Workshop on Market Design for helpful discussions. Detailed comments from a co-editor and anonymous referees significantly improved the paper. Yeon-Koo Che is grateful to the KSEF's World Class University Grant (R32-2008-000-10056-0) for financial support.


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.

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