Stable Matching with Mistaken Agents

TL;DR

This paper introduces the concept of robust equilibrium in large matching markets, showing that even with mistaken agents, outcomes remain close to stable matchings, impacting how preferences are estimated.

Contribution

It proposes the robust equilibrium concept for markets with mistaken agents and analyzes its implications on the outcomes of the Deferred Acceptance algorithm.

Findings

Almost all applicants may be non-truthful in robust equilibrium

Outcomes are arbitrarily close to stable matchings despite mistakes

Truth-telling is not necessary for near-stable outcomes

Abstract

Motivated by growing evidence of agents' mistakes in strategically simple environments, we propose a solution concept -- robust equilibrium -- that requires only an asymptotically optimal behavior. We use it to study large random matching markets operated by the applicant-proposing Deferred Acceptance (DA). Although truth-telling is a dominant strategy, almost all applicants may be non-truthful in robust equilibrium; however, the outcome must be arbitrarily close to the stable matching. Our results imply that one can assume truthful agents to study DA outcomes, theoretically or counterfactually. However, to estimate the preferences of mistaken agents, one should assume stable matching but not truth-telling.