Secretary Problems and Online Auctions

Years and Authors of Summarized Original Work

• 2004; Hajiaghayi, Kleinberg, Parkes

• 2008; Babaioff, Immorlica, Kempe, Kleinberg

• 2013; Bateni, Hajiaghayi, Zadimoghaddam

Problem Definition

The classic secretary problem, a prime example of stopping theory, has been studied extensively in the computer science literature. Consider the scenario where an employer is interested in hiring one secretary out of a pool of candidates. The difficulty is that, although the employer does not know the utility of a candidate before she is interviewed, the irrevocable hiring decision for each candidate has to be made right after the interview and prior to interviewing the subsequent candidates. The goal is nonetheless to pick the best candidate or maximize the probability of achieving this.

Optimization Angle

The above scenario is hopeless from an algorithmic point of view since an adversarial input makes it impossible to hire the best candidate. We can take either of two paths to make the problem...