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 strategy-proofness (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.
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