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

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

Abstract: This research investigates the possibility of collusion in unrepeated first-price auctions where the number of participants is uncertain. The study does not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are suppressed, and even allows for the existence of multiple cartels. The researchers 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. The study shows that bidding rings benefit ring centers and all agents, both members and non-members of bidding rings, at the auctioneer's expense. The techniques introduced in this paper may also be useful for reasoning about other problems involving asymmetric information.

Research Question: Can collusion be supported in unrepeated first-price auctions when the number of participants is uncertain?

Methodology: The researchers use game theory and mathematical modeling to analyze the problem. They consider scenarios where agents can form bidding rings and coordinate their bids to achieve a desired outcome. They assume that agents have incomplete information about the number of participants and can join or leave bidding rings based on strategic decisions.

Results: The study identifies a bidding ring protocol that results in an efficient allocation in Bayes-Nash equilibrium. This protocol allows non-colluding agents to bid straightforwardly, and colluding agents to join bidding rings when invited and truthfully declare their valuations to the ring center. The researchers show that bidding rings benefit ring centers and all agents, both members and non-members of bidding rings, at the auctioneer's expense.

Implications: The findings of this study have important implications for the design and conduct of auctions. They suggest that collusion can be supported in unrepeated first-price auctions even when the number of participants is uncertain. This knowledge can help auctioneers to develop rules and procedures that prevent collusion and ensure fair competition. Additionally, the techniques introduced in this paper may be useful for reasoning about other problems involving asymmetric information.

Link to Article: https://arxiv.org/abs/0201017v2 Authors: arXiv ID: 0201017v2