Collusion in auctions with externalities

In standard auctions, collusion among buyers eliminates bidding competition despite informational asymmetries. Collusion can, however, be imperfect when the situation involves "externalities" among buyers, that is, when a buyer is worse off if one rival wins the goon rather than if nobody gets it. For intermediate values of the externality and under various objective functions, the seller finds it optimal to design an auction that leads, in equilibrium, to a collusive outcome that is ex post inefficient for the group of buyers; an ex ante incentive-efficient collusion mechanism for the buyers is characterized in this situation.