Robust Tournaments

We characterize robust tournament design -- the prize scheme that maximizes the lowest effort in a rank-order tournament where the distribution of noise is unknown, except for an upper bound, H̄, on its Shannon entropy. The robust tournament scheme awards positive prizes to all ranks except the last, with a distinct top prize. Asymptotically, the prizes follow the harmonic number sequence and induce an exponential distribution of noise with rate parameter e-H̄. The robust prize scheme is highly unequal, especially in small tournaments, but becomes more equitable as the number of participants grows, with the Gini coefficient approaching $1/2$.