A first-price sealed-bid auction of an item for which bidders are risk-neutral and have privately known values is shown to have an equilibrium in mixed behavioral strategies if the joint distribution of bidders' values has a continuous density on a cubical support. Such an equilibrium has...

For an all-pay sealed-bid auction of an item for which each bidder's realized value can depend on every bidder's privately observed signal, existence of equilibria in behavioral strategies is established using only the assumption that bidders' value functions and the density function of signals...