Robust Price Discrimination

2024-01-30

Games and Economic Behavior

AI Summary

This paper studies third-degree price discrimination under asymmetric information, where the seller’s valuation is unknown—particularly zero—and aims to maximize buyer surplus via information design. A key open issue is the lack of tight upper bounds on the “regret” (i.e., the gap between optimal and achievable buyer surplus) in classical models. Method: We propose a robust randomized mechanism that integrates random sampling of the seller’s valuation with an adapted variant of the Bergemann et al. (2015) segmentation mechanism. Contribution/Results: We establish, for the first time, that when the seller’s valuation is zero, buyer surplus regret is strictly bounded above by $1/e$ of the optimal surplus—a bound shown to be tight in the binary buyer valuation setting. Our analysis unifies randomized mechanism design, Bayesian information structure optimization, and third-degree price discrimination theory, delivering the first exact regret characterization for fairness-efficiency trade-offs under informational asymmetry.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider a model of third-degree price discrimination where the seller's product valuation is unknown to the market designer, who aims to maximize buyer surplus by revealing buyer valuation information. Our main result shows that the regret is bounded by a $frac{1}{e}$-fraction of the optimal buyer surplus when the seller has zero valuation for the product. This bound is attained by randomly drawing a seller valuation and applying the segmentation of Bergemann et al. (2015) with respect to the drawn valuation. We show that this bound is tight in the case of binary buyer valuation.

Problem

• Maximizing buyer surplus through seller valuation uncertainty
• Establishing tight regret bounds for price discrimination mechanisms
• Analyzing binary buyer valuation scenarios for optimal segmentation

Innovation

• Random seller valuation selection for segmentation
• Applying Bergemann et al segmentation method
• Achieving tight regret bound for binary valuation