Optimal auctions under collusion of buyers with discrete valuations

Abstract. The potential seller of an indivisible good faces two potential buyers whose valuations for the good are private information. We derive the optimal selling mechanism under the assumption that the buyers collude both when the valuations are independently distributed and when they are correlated. We find that when the valuations are independent the seller can obtain the same expected revenue as if the buyers behaved noncooperatively; if instend the valuations are correlated then collusion harms the seller. In this latter case, moreover, each buyer’s information at the collusion stage about the other buyer’s valuation turns out to be very relevant for the effectiveness of collusion.