Bribing in first-price auctions

I study a symmetric 2-bidder IPV first-price auction prior to which one bidder can offer his rival a bribe in exchange for the latter's abstention. I focus on pure and undominated strategies, and on continuous monotonic equilibria-equilibria in which the bribing function is continuous and nondecreasing. When types are distributed continuously on the unit interval, such an equilibrium, if it at all exists, is necessarily trivial-its bribing function is identically zero. I provide a sufficient condition for its existence and sufficient conditions for its nonexistence. When the minimum type is strictly positive, a non-trivial equilibrium may exist, but it must be pooling. I provide a sufficient condition for the existence of such an equilibrium. When types are distributed continuously on the unit interval and dominated strategies are allowed, a non-trivial non-pooling equilibrium exists, at least under the uniform prior.