Protective Behavior in Matching Models

This paper analyzes the use of a version of lexical maximim strategies, called protective behavior, in two-sided matching models. It restricts attention to mechanisms which produce stable matchings, that is, matchings which are individually rational and pairwise optimal. The main results of the paper show that truth-telling is the unique form of protective behavior in two such mechanisms. The first is the one which selects the student-optimal stable matching in the college-admissions model, while the second is the mechanism which selects the buyer-optimal matching in the Shapley-Shubik assignment model.