Competition Complexity in Multi-Item Auctions: Beyond VCG and Regularity

2025-06-10

AI Summary

This paper studies the value of a monopolist’s bargaining power in multi-item auctions, introducing *competition complexity*—the number of additional bidders required by simple auctions to match the expected revenue of the optimal mechanism. Moving beyond VCG and standard regularity assumptions, we propose *α-strong regularity*, a novel distributional condition. Under this assumption, the competition complexity of separate sales improves from Ω(n·ln(m/n)) to Θ(n/α); for grand bundling, we obtain a constant upper bound with a single bidder and extend it to the first-best benchmark. Our analysis integrates tools from game theory, mechanism design, monotone hazard rate (MHR) analysis, and revenue–welfare comparisons. These results substantially reduce the sample complexity required to learn value distributions for near-optimal revenue in large markets: competition complexity for separate sales becomes tunable via α, while grand bundling achieves constant complexity under either small item counts or MHR distributions.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We quantify the value of the monopoly's bargaining power in terms of competition complexity--that is, the number of additional bidders the monopoly must attract in simple auctions to match the expected revenue of the optimal mechanisms (c.f., Bulow and Klemperer, 1996, Eden et al., 2017)--within the setting of multi-item auctions. We show that for simple auctions that sell items separately, the competition complexity is $Theta(frac{n}{alpha})$ in an environment with $n$ original bidders under the slightly stronger assumption of $alpha$-strong regularity, in contrast to the standard regularity assumption in the literature, which requires $Omega(n cdot ln frac{m}{n})$ additional bidders (Feldman et al., 2018). This significantly reduces the value of learning the distribution to design the optimal mechanisms, especially in large markets with many items for sale. For simple auctions that sell items as a grand bundle, we establish a constant competition complexity bound in a single-bidder environment when the number of items is small or when the value distribution has a monotone hazard rate. Some of our competition complexity results also hold when we compete against the first best benchmark (i.e., optimal social welfare).

Problem

• Quantify monopoly bargaining power via competition complexity in multi-item auctions
• Compare revenue of simple auctions versus optimal mechanisms under strong regularity
• Establish constant competition complexity bounds for grand bundle auctions

Innovation

• Quantify monopoly bargaining via competition complexity
• Use Θ(n/α) complexity under α-strong regularity
• Establish constant complexity for grand bundle auctions