Sequential round-robin tournaments with multiple prizes

We examine the fairness and intensity of sequential round-robin tournaments with multiple prizes heterogeneous players. A tournament is called fair if winning probabilities in each match depend only on players' characteristics but not sequence matches. show that three players will be second prize valued half first prize. The optimal structure may, however, subject to a trade-off between (measured by expected aggregate effort). By contrast, there no for which more than matches exogenously fixed. Our analysis suggests many major sporting events are inherently unfair.