Bidding Rings in Privatization

This paper studies privatization problems, in which a social planner sells an indivisible object to one of the agents with private valuations (types), and explains the coexistence of auctions and consortia in practice with cooperative incentive in collusive bidding behaviors. By using the theory of optimal mechanism design with dominant strategy equilibria, we show the universal existence of bidding rings (entities that exercise collusive bidding in practice) without any restriction of independent types as in the literature of collusive bidding. Our finding of bidding rings is for generalized Vickrey auctions, which are similar to the Vickrey auction except that the payment of the winner depends not only on the second highest bid but also on other non-winners’ bids. We lay out our main result for a Vickrey auction without a reserve price from the ‘mechanism design approach,’ while postponing the result for a Vickrey auction with a reserve price from the ‘auction design approach.’ In brief, we find that the optimal mechanism is a generalized Vickrey auction without a reserve price, that it is vulnerable to the bidding ring of a Groves scheme, and that the bidding ring can be established as a consortium to avoid collusive bidding.