Despite their importance, games with incomplete information and dependent types are poorly understood; only special cases have been considered and a general approach is not yet available. In this paper, we propose a new condition (named richness) for correlation of types in (asymmetric) Bayesian...

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which...

We study equilibria in second price auctions when bidders are independently and privately informed about both their values and participation costs and their joint distributions across bidders are not necessarily identical. We show that there always exists an equilibrium in this general setting...