Stable Matching Mechanisms are Not Obviously Strategy-Proof

TL;DR

This paper demonstrates that no stable matching mechanism can be 'obviously strategy-proof' for any side, despite the widespread use of strategy-proof algorithms like deferred acceptance, and introduces a new mechanism under certain preference conditions.

Contribution

It proves the impossibility of stable mechanisms being obviously strategy-proof and presents a new mechanism that achieves this property when preferences are acyclical.

Findings

No stable matching mechanism is obviously strategy-proof for any side.

Empirical evidence shows applicants often misrepresent preferences despite strategy-proof mechanisms.

A new stable mechanism is introduced that is obviously strategy-proof under acyclical preferences.

Abstract

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.