Punishment and Accuracy Level in Contests

of the Thesis In the literature on contests, punishments have received much less attention than prizes. One possible reason is that punishing the bottom player(s) in a contest where all contestants are not allowed to quit, while e¤ective in increasing contestants’total e¤ort, often violates individual rationality constraints. But what will happen in an open contest where all potential contestants can choose whether or not to participate? In chapter 1, we study a model of this type and allow the contest designer to punish the bottom participant according to their performances. We conclude that punishment is often not desirable (optimal punishment is zero) when the contest designer wants to maximize the expected total e¤ort, while punishment is often desirable (optimal punishment is strictly positive) when the contest designer wants to maximize the expected highest individual e¤ort. In the literature on imperfectly discriminating contests, researchers normally assume that the contest designer has a certain level of accuracy in choosing the winner, which can be represented by the discriminatory power r in the Power Contest Success Function (the Power CSF, proposed by Tullock in 1980). With symmetric contestants, it is well known that increasing accuracy (r) always increases total e¤ort when the pure-strategy equilibrium exists. In chapter 2, we look at the cases where the contestants are heterogeneous in ability. We construct an equilibrium set on r > 0, where a unique pure-strategy equilibrium exists for any r below a critical value and a mixed-strategy equilibrium exists for any r above this critical value. We …nd that if the contestants are su¢ ciently di¤erent in ability, there always exists an optimal accuracy level for the contest designer. Additionally, as we increase the di¤erence in their abilities, the optimal accuracy level decreases. The above conclusions provide an explanation to many phenomena in the real world and may give guidance in some applications. In chapter 3, we propose the Power Contest Defeat Function (the Power CDF)