Comparative Statics and Welfare in Heterogeneous Contests: Bribes, Caps, and Performance Thresholds

Comparative statics for contests with two privately informed and ex ante heterogeneous contestants are analyzed. Strategies and payoffs are examined and it is shown that total effort may increase when one contestant becomes weaker. The second part of the paper considers dynamic contests in which one bidder may endogenously be revealed to be weak. For example, the first contestant has the possibility of preempting the contest by paying a bribe or taking some other action. If the bribe is not paid the second contestant infers the first contestant is relatively weak or uninterested. Adding the possibility of paying a preemptive bribe decreases expected payoff for a set of types of at least one of the contestants, possibly the contestant who is ostensibly advantaged by the option to preempt the contest. However, the payoff of the recipient of the effort and the ex ante payoff of both contestants may improve.