Incentives and Strategic Choices In The Secretary Problem
Optimal policies for various secretary problems have an undesirable trait: they would interview applicants for the position, but those earlier ones are guaranteed to not get selected. Therefore, early applicants have incentive to not come in for their scheduled interviews, and as a direct consequence, the employer's intention to learn from the population becomes useless. Prior works have been done that tried to mitigate this issue, where the employer sacrifices her overall probability of selecting the best applicant by assigning equal selection probability to all interview slots. Among our results, we show such approaches can be costly for an employer with objectives different from the classical one. Furthermore, we generalize the classical setting to allow applicants to make independent choices with regard to their time of availability. This new game-theoretic approach solves the interviewing-without-hiring problem that arose earlier, and surprisingly, improves the employer's probability of selecting the best applicant from one obtained in the classical setting.