[Paper Review] Stable Matching Mechanisms are Not Obviously Strategy-Proof

Itai Ashlagi, Yannai A. Gonczarowski|arXiv (Cornell University)|Nov 2, 2015

Game Theory and Voting Systems19 citations

TL;DR

This paper demonstrates that no stable matching mechanism is obviously strategy-proof (OSP) for either side of a two-sided market, even though the deferred acceptance (DA) algorithm is strategy-proof for applicants. It proves that OSP—requiring strategy-proofness to be transparent without contingent reasoning—is incompatible with stability, and introduces a novel OSP mechanism for stable matchings only when the non-proposing side has 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.

Motivation & Objective

• To investigate whether stable matching mechanisms can be designed to be obviously strategy-proof (OSP), a stronger incentive property than standard strategy-proofness.
• To resolve the open question of whether the deferred acceptance (DA) mechanism, widely used in school choice and labor markets, can be implemented in a way that makes its strategy-proofness cognitively transparent.
• To explore the cognitive complexity of strategic reasoning in stable mechanisms and explain why sequential implementations, despite weaker incentive properties, may still lead to more sincere behavior.
• To characterize conditions under which an OSP mechanism for stable matchings can be constructed, focusing on acyclical preferences on one side of the market.

Proposed method

• Adopts the notion of obvious strategy-proofness (OSP) introduced by Li (2017), which requires that strategy-proofness be verifiable without contingent reasoning.
• Analyzes the structural limitations of stable mechanisms by proving that no mechanism implementing a stable matching can be OSP for any side of the market.
• Constructs a novel sequential mechanism that implements a stable matching and is OSP for applicants when the non-applicant side has acyclical preferences.
• Uses the concept of acyclical preferences (Ergin, 2002) to define a domain where OSP stability is achievable, generalizing from serial dictatorship in perfectly aligned preference cases.
• Compares static and sequential implementations of DA, showing that sequential versions are not OSP but reduce cognitive load and improve sincerity in practice.
• Employs formal game-theoretic analysis to prove that OSP is incompatible with stability due to the two-sided nature of stability constraints.

Experimental results

Research questions

• RQ1 Can any stable matching mechanism be obviously strategy-proof for either side of a two-sided market?
• RQ2 Why do participants in real-world matching markets still misreport preferences despite the use of strategy-proof mechanisms like deferred acceptance?
• RQ3 Is there a domain restriction—such as acyclical preferences—under which an obviously strategy-proof stable mechanism can be constructed?
• RQ4 How do sequential implementations of DA affect strategic behavior, even though they are not OSP?
• RQ5 What explains the empirical observation that sequential DA leads to more sincere reporting than static DA, despite weaker incentive properties?

Key findings

• No mechanism that implements a stable matching can be obviously strategy-proof for any side of the market, establishing a fundamental incompatibility between stability and OSP.
• An obviously strategy-proof mechanism for stable matchings exists when agents on the non-proposing side have acyclical preferences, providing a constructive solution under a specific domain restriction.
• The deferred acceptance mechanism, while strategy-proof, is not obviously strategy-proof, meaning its incentive properties are not transparent to participants without complex reasoning.
• Sequential implementations of DA reduce cognitive load and encourage sincere behavior, even though they are not OSP and may not even make sincerity a dominant strategy.
• The cognitive complexity of reasoning about stable mechanisms explains why participants may misreport preferences even when truth-telling is optimal.
• The results suggest that while OSP mechanisms are not feasible for general stable matching, sequential mechanisms serve as a practical alternative by simplifying decision-making without sacrificing stability.