We provide conditions that simplify applying Reny's (1999) better-reply security to Bayesian games, and use these conditions to prove the existence of equilibria for classes of games in which payoff discontinuities arise only at "ties." These games include a general version of all-pay contests,...

Many sales, sports, and research contests are put in place to maximize contestants' performance. We investigate and provide a complete characterization of the prize structures that achieve this objective in settings with many contestants. The contestants may be ex-ante asymmetric in their...

We propose adding a third,intermediate,verdict to the two-verdict used in criminal trials. We show that the additional verdict can be used to distinguish between convicted defendants, based on the residual doubt regarding their guilt at the end of the trial, in a way that improves welfare and...