Weak cartels and collusion-proof auctions

We study private value auctions in which bidders may collude without using side-payments. In our model, bidders coordinate their actions to achieve an outcome that interim-Pareto dominates the noncooperative outcome. We characterize auctions that are collusion-proof in the sense that no such coordination opportunities exist, and show that the efficient and revenue maximizing auctions are not collusion-proof unless all bidders exhibit a concave distribution of valuations. We then solve for revenue maximizing collusion-proof auctions. If distributions of valuations are symmetric and single-peaked, the optimal selling mechanism is a standard auction with a minimum bid, followed by sequential negotiation in case no bidder bids above the minimum bid.