Fair competition design

We study the impact of two basic principles of fairness on the structure of competition systems and perform our analysis by focusing on sports competitions. The first principle states that equally strong players should have the same chances of being the final winner, while the second principle requires that the competition system should not favor weaker players. We apply these requirements to a class of competitions which includes, but is not limited to, the sport tournament systems that are most commonly used in practice, such as round-robin tournaments and different kinds of knockout competitions, and we characterize the structures satisfying these requirements. In our results, a new competition structure that we call an antler is found to play a referential role. Finally, we show that the class of fair competition systems becomes rather small when both fairness principles are jointly applied.