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Candidates arrive sequentially for an interview process which results in thembeing ranked relative to their predecessors. Based on the ranks available ateach time, one must develop a decision mechanism that selects or dismisses thecurrent candidate in an effort to maximize the chance to select the best. Thisclassical version of the ``Secretary problem'' has been studied in depth usingmostly combinatorial approaches, along with numerous other variants. In thiswork we consider a particular new version where during reviewing one is allowedto query an external expert to improve the probability of making the correctdecision. Unlike existing formulations, we consider experts that are notnecessarily infallible and may provide suggestions that can be faulty. For thesolution of our problem we adopt a probabilistic methodology and view thequerying times as consecutive stopping times which we optimize with the help ofoptimal stopping theory. For each querying time we must also design a mechanismto decide whether we should terminate the search at the querying time or not.This decision is straightforward under the usual assumption of infallibleexperts but, when experts are faulty, it has a far more intricate structure.

Optimal Stopping Methodology for the Secretary Problem with Random Queries