The Hiring Problem and Lake Wobegon Strategies

We introduce the hiring problem, in which a growing company continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite difierent from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of decision making under uncertainty and has many possible applications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring prob- lem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically signiflcant modiflcations. We demonstrate several intriguing behaviors of the two strategies. Speciflcally, we show dramatic difierences between hiring above the mean and above the median. We also show that both strategies are intrinsically connected to the lognormal distribution, leading to only very weak concentration results, and the marked importance of the flrst few hires on the overall outcome.