We study round-robin tournaments with three players whose values of winning are common knowledge. In every stage a pair-wise match is modelled as an all-pay auction. The player who wins in two matches wins the tournament. We characterize the sub-game perfect equilibrium for symmetric (all...

We study the classical Tullock's model of one-stage contests where the probability of winning is a function of the efforts exerted by the contestants. We show that by a simple non-discriminating rule the contest designer is able to manipulate the outcome of the contest such that the...

We study a three-stage all-pay auction with two players in which the first player to win two matches wins the best-of-three all-pay auction. The players have values of winning the contest and may have also values of losing, the latter depending on the stage in which the contest is decided. It is...

We study all-pay contests under incomplete information where the reward is a function of the contestant's type and effort. We analyse the optimal reward for the designer when the reward is either multiplicatively separable or additively separable in effort and type. In the multiplicatively...

We study all-pay contests in which there is a positive probability of a tied outcome. We analyse both one-stage contests and multi-stage contests with tie-breaks. We demonstrate that in symmetric two-player contests, the designer does not have an incentive to award a prize in a case of a tie....