Another good one from Scott Ogawa. It’s the Creampuff Dilemma. A college football coach has to set its pre-season non-conference schedule, thinking ahead to the end-of-season polling that decides Bowl Bids. A schedule stocked with creampuffs means lots of easy wins. But holding fixed the number of wins, a tough schedule will bolster your ranking.
Here’s Scott’s model. Each coach picks a number p between 0 and 1. He is successful (s=1) with probability p and unsuccessful (s=0) with probability 1-p. These probabilities are independent across players. (Think of these as the top teams in separate conferences. They will not be playing against each other.)
Highest s-p wins.