Abstract
This paper studies the optimal-ring-size problem in a first-price auction environment, where a collusive ring center can endogenously choose the number of its members. The key finding is that, contrary to the results for second-price auctions, the optimal ring at first-price auctions is generally not all-inclusive, especially when the number of bidders is large. Outsiders can free-ride the ring's suppressed competition and earn higher payoffs than by being a ring member; hence they choose not to participate in collusion. As a partial ring creates bidder asymmetry at first-price auctions, the overall allocation will be inefficient, which provides a basis for laws that outlaw collusion in auctions.
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