Strategyproofness in the large as a desideratum for market design

We propose a criterion of approximate strategyproofness (SP), called strategyproof in the large (SP-L). A mechanism is SP-L if, for any agent, any probability distribution of the other agents' reports, and any > 0, in a large enough market the agent maximizes his expected payo to within by reporting his preferences truthfully. Conceptually, SP-L distinguishes between two kinds of non-SP mechanisms: those where pro table misreports vanish as the market grows large in our sense, and those where pro table misreports persist even for agents who regard the mechanism's prices as exogenous. Our main result shows that, under some assumptions, SP-L is approximately costless to satisfy in large markets relative to Bayes-Nash or Nash implementability. The assumptions include anonymity, private values, and a continuity condition. We interpret the result as justifying SP-L as a second-best desideratum, especially for problems for which the bene ts of SP design are compelling (e.g., compliance with the Wilson doctrine) yet it is known that mechanisms that are exactly SP are unattractive. We illustrate with examples from assignment, auctions, and matching. ∗For helpful discussions we are grateful to Nabil Al-Najjar, Susan Athey, Aaron Bodoh-Creed, Gabriel Carroll, Je Ely, Alex Frankel, Drew Fudenberg, Matt Gentzkow, Jason Hartline, John Hat eld, Richard Holden, Ehud Kalai, Emir Kamenica, Fuhito Kojima, Scott Kominers, Jacob Leshno, Jon Levin, Paul Milgrom, Roger Myerson, David Parkes, Parag Pathak, Nicola Persico, Andy Postlewaite, Canice Prendergast, Ilya Segal, Eran Shmaya, Lars Stole, Glen Weyl, and especially Al Roth. We are grateful to seminar audiences at Ohio State, the MFI Conference on Matching and Price Theory, UCLA, Chicago, AMMA 2011, Boston College, the NBER Conference on Market Design, Duke / UNC, Michigan, Carnegie Mellon / Pittsburgh, Montreal, Berkeley, Northwestern and Rochester. †Harvard University, azevedo@fas.harvard.edu. ‡University of Chicago Booth School of Business, eric.budish@chicagobooth.edu. STRATEGYPROOFNESS IN THE LARGE 1

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