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

TL;DR

This paper analyzes the strategic formation and stability of bidding rings in unrepeated first-price auctions with uncertain participant numbers, revealing that such collusion can be efficient and beneficial for involved agents.

Contribution

It introduces a bidding ring protocol that supports equilibrium collusion without perfect information, allowing for multiple cartels and strategic joining decisions.

Findings

Bidding rings can be supported in equilibrium without perfect knowledge.

The protocol leads to efficient allocation and benefits all agents.

Collusion benefits both ring members and non-members at the auctioneer's expense.

Abstract

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.