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. 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 collusive public perfect equilibria that allow the seller to extract the entire surplus from the buyers in the limit as the buyers' discount factor goes to 1. I therefore show that a non-committed seller can effectively fight collusion even when she faces patient buyers, can only set reserve prices, and has to satisfy stringent public disclosure requirements.
We study mechanism design with flexible but costly information acquisition. There is a principal and four or more agents, sharing a common prior over a set of payoff-relevant states. The principal proposes a mechanism to the agents who can then acquire information about the state by privately designing a signal device. As long as it is costless for each agent to acquire a signal that is independent from the state, there exists a mechanism which allows the principal to implement any social choice rule at zero information acquisition cost to the agents.