Description:
This paper presents new results on the existence of Bayesian equilibria in pure strategies of a specified functional form. These results broaden the scope of methods developed by Reny (2011) well beyond monotone pure strategies. Applications include natural models of first-price and all-pay auctions not covered by previous existence results. To illustrate the scope of our results, we present two applications to auctions: (i) a first-price auction in which bidders' payoffs have a very general interdependence structure; and (ii) an all-pay auction with non-monotone equilibrium