We study a game between N job applicants who incur a cost \(c\in [0,1)\) (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best applicant. We define a full learning equilibrium and prove its existence, uniqueness, and optimality. In full learning equilibrium, the administrator accepts the current best applicant n with probability c if \(n<n^*\) and with probability 1 if \(n\ge n^*\) for a threshold \(n^*\) independent of c. In contrast to the case without cost, where the success probability converges to \(1/\textrm{e}\approx 0.37\) as N tends to infinity, with cost the success probability decays like \(N^{-c}\) .
