Collusion in Unrepeated, First-Price Auctions with an Uncertain Number of Participants

We consider the question of whether collusion among bidders (a "bidding ring") can be supported in equilibrium of unrepeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and Marx [2007], we do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are suppressed by the bidding ring, and indeed even allow for the existence of multiple cartels. Furthermore, while we treat the association of bidders with bidding rings as exogenous, we allow bidders to make strategic decisions about whether to join bidding rings when invited. We identify a bidding ring protocol that results in an efficient allocation in Bayes{Nash equilibrium, under which non-colluding agents bid straightforwardly, and colluding agents join bidding rings when invited and truthfully declare their valuations to the ring center. We show that bidding rings benefit ring centers and all agents, both members and non-members of bidding rings, at the auctioneer's expense. The techniques we introduce in this paper may also be useful for reasoning about other problems in which agents have asymmetric information about a setting.

[1]  R. Preston McAfee.  Endogenous Availability, Cartels, and Merger in an Equilibrium Price Dispersion , 1994 .

[2]  P. Klemperer.  Auction Theory: A Guide to the Literature , 1999 .

[3]  T. Ungern-Sternberg,et al.  Cartel Stability in Sealed Bid Second Price Auctions , 1988 .

[4]  Jonathan S. Feinstein,et al.  Asymmetric Information and Collusive Behavior in Auction Markets , 1985 .

[5]  D. Graham,et al.  Collusive Bidder Behavior at Single-Object Second-Price and English Auctions , 1987, Journal of Political Economy.

[6]  Peter Cramton,et al.  Cartel Enforcement with Uncertainty About Costs , 1990 .

[7]  Marc S. Robinson,et al.  Collusion and the Choice of Auction , 1985 .

[8]  George J. Mailath,et al.  Collusion in second price auctions with heterogeneous bidders , 1991 .

[9]  Ronald M. Harstad,et al.  Equilibrium bid functions for auctions with an uncertain number of bidders , 1990 .

[10]  D. Fudenberg,et al.  Digitized by the Internet Archive in 2011 with Funding from Working Paper Department of Economics the Folk Theorem with Imperfect Public Information , 2022 .

[11]  Moshe Tennenholtz,et al.  Bidding clubs: institutionalized collusion in auctions , 2000, EC '00.

[12]  Robert H. Porter,et al.  Collusion in Auctions , 1989 .

[13]  Masaki Aoyagi,et al.  Bid rotation and collusion in repeated auctions , 2003, J. Econ. Theory.

[14]  J. Richard,et al.  Differential Payments within a Bidder Coalition and the Shapley Value , 1990 .

[15]  R. McAfee,et al.  Auctions with a stochastic number of bidders , 1987 .

[16]  J. Asker,et al.  Bidding Rings , 2022 .

[17]  Andrzej Skrzypacz,et al.  Tacit collusion in repeated auctions , 2001, J. Econ. Theory.