Abstract

In a problem described by the economist Martin Weitzman in 1979 an agent is presented with boxes containing prizes. She may open boxes in any order, discovering prizes within, and optimally stop. She wishes to maximize the expected value of the greatest prize found, minus costs of opening boxes. The problem has an attractive solution by means of a so-called Pandora rule, and has applications to searching for a house or job. However, it does not address the problem of a student who searches for the subject to choose as her major and benefits from the courses she takes while searching.

So motivated, we ask whether there are any problems for which a Pandora rule is optimal when the utility is a more general function of all the discovered prizes. We explain how the Gittin index theorem can be used to solve one version of the student’s problem. This is not the full story, since we can also describe some problems which are not of multi-armed bandit type and yet for which a Pandora rule is optimal. (Joint work with Wojciech Olszewski, Dept Economics, Northwestern University.)