The Gas Station Problem and Applications by Kai Jackson '25

The Gas Station Problem and Applications by Kai Jackson ’25, Wednesday April 16, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Statistics Colloquium

The Gas Station Problem is a classic problem in probability and decision theory. Also known as the secretary problem or the marriage problem, among other names, it is a simple setup in which one seeks an optimal stopping point. The setup for the problem involves a set of n options which can be ranked but do not have a known distribution, with the goal of choosing the best one. In choosing, one is restricted to only immediately accepting or rejecting each option before seeing the values of the rest. The problem then becomes determining how much information is needed from seeing earlier options to maximize the probability of making the best choice. This relatively simple setup results in a beautiful solution and can be modified and generalized in many ways to have a variety of useful applications.