Efficient Ex Post Implementable Auctions and English Auctions for Bidders with Non-Quasilinear Preferences

We study efficient auction design for a single indivisible object when bidders have interdependent values and non-quasilinear preferences. Instead of quasilinearity, we assume only that bidders have positive wealth effects. Our setting nests cases where bidders are ex ante asymmetric, face financial constrains, are risk averse, and/or face ensuing risk. We give necessary and sufficient conditions for when there exists an ex post implementable and (ex post Pareto) efficient mechanism. Necessary and sufficient conditions for the existence of efficient ex post implementable mechanisms differ between the case where the object is a good and when the object is a bad. In the good setting, there is an efficient ex post implementable mechanism if there is an efficient ex post implementable mechanism in a corresponding quasilinear setting. This result extends established results on efficient ex post equilibria of English auctions with quasilinearity to our non-quasilinear setting. Yet, in the bad setting (i.e. a procurement auction) there is no mechanism that has an ex post efficient equilibrium if the level of interdependence between bidders is sufficiently strong. This result holds even if bidder costs satisfy standard crossing conditions that are sufficient for efficient ex post implementation in the quasilinear setting.