Publication Date: August 2019
Revision Date: November 2019
This paper presents new results on the existence of pure-strategy Bayesian equilibria in speciﬁed functional forms. 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 provide an analysis of three auctions: (i) a ﬁrst-price auction of objects that are heterogeneous and imperfect substitutes; (ii) a ﬁrst-price auction in which bidders’ payoﬀs have a very general interdependence structure; and (iii) an all-pay auction with non-monotone equilibrium.
Keywords: Bayesian games, Monotone strategies, Pure-strategy equilibrium, Auctions
JEL Classification Codes: C72, D44CFDP 2190