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,...

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...

Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied whenever possibleʺ. We show that there are games in which it is not clear what whenever possibleʺ means. Then, we provide a simple...