Document Type

Discussion Paper

Publication Date


CFDP Number


CFDP Revision Date

March 1, 2020

CFDP Pages


Journal of Economic Literature (JEL) Code(s)

C72, D44


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.

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