Full Surplus Extraction From Colluding Bidders

I consider a repeated auction setting with colluding buyers and a seller who adjusts reserve prices over time without long-term commitment. To model the seller’s concern for collusion, I introduce a new equilibrium concept: collusive public perfect equilibrium (cPPE). For every strategy of the seller I define the corresponding “buyer-game” in which the seller is replaced by Nature who chooses the reserve prices for the buyers in accordance with the seller’s strategy. A public perfect equilibrium is collusive if the buyers cannot achieve a higher symmetric public perfect equilibrium payoff in the corresponding buyer-game. In a setting with symmetric buyers with private binary iid valuations and publicly revealed bids, I find a collusive public perfect equilibrium that allows the seller to extract the entire surplus from the buyers in the limit as the discount factor goes to 1. I therefore show that a patient, non-committed seller can effectively fight collusion even when she can only set reserve prices and has to satisfy stringent public disclosure requirements.