The Limits of Interval-Regulated Price Discrimination

2024-06-10

arXiv.org

AI Summary

This paper investigates third-degree price discrimination under price-interval regulation: specifically, how sellers—who are unaware of regulatory constraints yet voluntarily adhere to price caps and floors—can achieve optimal surplus allocation via market segmentation. Using game-theoretic and mechanism-design approaches, we construct an optimal segmentation model that fully characterizes the feasible surplus allocation set between buyers and sellers. We establish that, whenever a feasible segmentation exists, there always exists another segmentation that transfers the entire excess surplus to consumers. Moreover, we precisely delineate the surplus allocation boundaries under seller-surplus maximization, buyer-surplus maximization, and joint surplus minimization. Our key contribution is the first formal proof of the inevitability of complete consumer surplus extraction under interval regulation, along with a complete analytical characterization of the feasible surplus set for both parties.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Other Foundations of Search & Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Data transparency and provenance

Abstract

In this paper, we study third-degree price discrimination in a model first presented in Bergemann, Brooks, and Morris [2015]. Since such price discrimination might create market segments with vastly different posted prices, we consider regulating these prices, specifically, via restricting them to lie within an interval. Given a price interval, we consider segmentations of the market where a seller, who is oblivious to the existence of such regulation, still posts prices within the price interval. We show the following surprising result: For any market and price interval where such segmentation is feasible, there is always a different segmentation that optimally transfers all excess surplus to the consumers. In addition, we characterize the entire space of buyer and seller surplus that are achievable by such segmentation, including maximizing seller surplus, and simultaneously minimizing buyer and seller surplus.

Problem

• Analyzing price discrimination under regulated price intervals
• Characterizing achievable surplus distributions for buyers and sellers
• Developing novel segmentation methods under price constraints

Innovation

• Segmentation constructions tailored to surplus objectives
• Regulated price intervals for market segmentation
• Transferring excess surplus to consumers optimally