Collusion enforcement in repeated first-price auctions

In the context of repeated first-price auctions, we explore how a bid-rigging cartel can simultaneously overcome the difficulty of soliciting truthful private information about valuations and the difficulty of enforcing its internal mechanism. Focusing on the class of trigger-strategy collusive agreements, we explicitly characterize the optimal collusive agreement for any given discount factor. Making use of the characterization, we also explore how a long-run seller can use a reserve price to fight the cartel.