Strategy-Proofness in the Large

Abstract

We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategyproofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism's "prices" as exogenous to her report -be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism -has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (i) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (ii) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate strategy-proofness, which evaluates incentives to manipulate ex post, and the traditional notion of approximate Bayes-Nash incentive compatibility, which evaluates incentives to manipulate ex interim with respect to the single common-knowledge probability distribution associated with Bayes-Nash equilibrium. * First version: October 2011. We thank the editor and four anonymous referees for comments and suggestions that improved the paper considerably. We are grateful to

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“…Azevedo and Budish (2013) argue that manipulation incentives disappear in deferred acceptance mechanisms as the market grows, though.…”

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“…We can also apply PS to student assignment with neighborhood priorities (Che & Kojima, ). Since PS is strategy proof in the large market (Azevedo & Budish, ) and by the asymptotic equivalence between PS and RP (Che & Kojima, ), we can apply similar argument to both RP and PS to analyze an approximately truth‐telling school choice equilibrium. For school priority, associate PS (or RP) with , where each is the eating speed of priority class .…”

Strategy-proofness in the Large

“…In the working paper version of this article (Azevedo and Budish, 2016), we show that a weaker version of Theorem 2 obtains under a condition that we call quasi-continuity. Quasicontinuity allows for the desired social choice function to have discontinuities, with respect to both the prior and the empirical distribution of reports, but requires that the discontinuities are in a certain sense knife-edge.…”