Fair elimination-type competitions

Abstract

We study the impact of two basic principles of fairness on the structure of elimination-type competitions and perform our analysis by focusing on sports competitions. The first principle states that stronger players should have a larger chance of winning than weaker players, while the second principle provides equally strong players the same chances of being the final winner. We apply these requirements to different kinds of knockout competitions, and characterise the structures satisfying them. In our results, a new competition structure that we call an antler is found to play a referential role.