  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.
