Stable Matching Mechanisms are Not Obviously Strategy-Proof

Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a growing amount of empirical evidence reveals that applicants misrepresent their preferences when this mechanism is used. This paper shows that no mechanism that implements a stable matching is "obviously strategy-proof" for any side of the market, a stronger incentive property than strategy-proofness that was introduced by Li (2017). A stable mechanism that is obviously strategy-proof for applicants is introduced for the case in which agents on the other side have acyclical preferences.