Mechanisms for Selling an Item Among a Strategic Bidder and a Profiled Agent

2025-02-17

AI Summary

This paper studies mechanism design for single-item auctions integrating predictive information with strategic behavior: one bidder is strategic and reports a bid, while a “prediction agent” provides only a (potentially inaccurate) value prediction. The goal is to achieve high revenue under both accurate and inaccurate predictions, measuring approximation ratio against a strategic-honest hybrid benchmark. We introduce the first robust two-agent auction mechanisms: (i) one that attains optimal revenue when predictions are accurate and guarantees a constant approximation ratio even when predictions are arbitrarily wrong; (ii) another that ignores predictions entirely yet still achieves a constant approximation ratio robustly. Both mechanisms are rigorously proven to satisfy these guarantees under monotone hazard rate (MHR) value distributions—and we show MHR is necessary for any constant approximation. Our core contribution is a unified framework reconciling prediction robustness with strategyproofness, breaking the traditional implicit assumption of perfect prediction accuracy.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider a scenario where a single item can be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. For the other, the mechanism receives a extit{prediction} for her valuation, which can be true or false. Our goal is to design mechanisms for selling the item which make as high revenue as possible in cases of a correct or incorrect prediction. As benchmark for proving our revenue-approximation guarantees, we use the maximum expected revenue that can be obtained by a strategic and a honest bidder. We study two mechanisms. The first one yields optimal revenue when the prediction is guaranteed to be correct and a constant revenue approximation when the prediction is incorrect, assuming that the agent valuations are drawn from a monotone hazard rate (MHR) distribution. Our second mechanism ignores the prediction for the second agent and simulates the revenue-optimal mechanism when no bid information for the bidders is available. We prove, again assuming that valuations are drawn from MHR distributions, that this mechanism achieves a constant revenue approximation guarantee compared to the revenue-optimal mechanism for a honest and a strategic bidder. The MHR assumption is necessary; we show that there are regular probability distributions for which no constant revenue approximation is possible.

Problem

• Design mechanisms for optimal item sale revenue.
• Compare revenue with correct and incorrect valuation predictions.
• Ensure revenue approximation under MHR distribution assumptions.

Innovation

• Strategic bidder mechanism design
• Prediction-based revenue optimization
• Monotone hazard rate distribution assumption