Distributionally Robust Auction Design with Deferred Inspection

2025-06-05

AI Summary

This paper studies distributionally robust auction mechanism design under delayed verification: how to maximize expected revenue or minimize regret under the worst-case joint distribution of bidders’ valuations and subsequent sales, when the seller faces ambiguity about these distributions. Departing from the standard common-prior assumption, this work is the first to integrate distributionally robust optimization into the delayed-verification mechanism design framework. We construct two classes of analytically optimal mechanisms—those with concave allocation rules paired with linear payment rules, and those paired with the maximum-payment rule—and prove that monotone optimal mechanisms need not exist in multi-bidder settings. Theoretically, linear-payment mechanisms achieve distributional robustness and are optimal under the worst-case distribution, whereas maximum-payment mechanisms significantly improve expected revenue under non-worst-case distributions, offering both theoretical guarantees and practical applicability.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Distributed Search

Application Category

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

Abstract

Mechanism design with inspection has received increasing attention due to its applications in the field. For example, large warehouses have started to auction scarce capacity. This capacity shall be allocated in a way that maximizes the seller's revenue. In such mechanism design problems, the seller can inspect the true value of a buyer and his realized sales in the next period without cost. Prior work on mechanism design with deferred inspection is based on the assumption of a common prior distribution. We design a mechanism with a deferred inspection that is (distributionally) robustly optimal either when the ambiguity-averse mechanism designer wants to maximize her worst-case expected payoff or when she wants to minimize her worst-case expected regret. It is a relatively simple mechanism with a concave allocation and linear payment rules. We also propose another robustly optimal mechanism that has the same concave allocation function but extracts the maximal payment from all the types of the agent, which can have a strictly higher expected payoff under non-worst-case distributions compared to the robustly optimal mechanism with the linear payment rule. We show that multi-bidder monotonous mechanisms might not exist.

Problem

• Design robust auction mechanism with deferred inspection
• Maximize seller revenue under distributional ambiguity
• Optimize worst-case payoff or minimize regret scenarios

Innovation

• Distributionally robust deferred inspection mechanism
• Concave allocation with linear payment rules
• Maximal payment extraction from all agent types