Bundling against Learning

2025-09-19

AI Summary

This paper studies optimal mechanism design for a monopolist seller facing a multi-dimensional buyer who endogenously acquires information about item values. The buyer first selects a one-dimensional linear signal to learn about the goods’ valuations; the seller then designs an incentive-compatible mechanism, resulting in a Bayesian Nash equilibrium between the two parties. Under a generalized Gaussian environment, we establish that all equilibria exhibit a vertical learning structure—where the buyer prioritizes learning about higher-order items—and yield posterior means that are comonotonic. Crucially, every equilibrium outcome can be fully implemented by a nested bundling mechanism, uncovering a fundamental equivalence between information acquisition and bundling. This result provides the first systematic characterization of the intrinsic correspondence between learning strategies and mechanism forms, offering a novel paradigm for multidimensional information design.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

A monopolist sells multiple goods to an uninformed buyer. The buyer chooses to learn any one-dimensional linear signal of their values for the goods, anticipating the seller's mechanism. The seller designs an optimal mechanism, anticipating the buyer's learning choice. In a generalized Gaussian environment, we show that every equilibrium has vertical learning where the buyer's posterior means are comonotonic, and every equilibrium is outcome-equivalent to nested bundling where the seller offers a menu of nested bundles. In equilibrium, the buyer learns more about a higher-tier good, resulting in a higher posterior variance on the log scale.

Problem

• Designing optimal mechanisms for selling multiple goods to uninformed buyers
• Analyzing buyer learning choices about product values in monopolistic settings
• Studying equilibrium outcomes with vertical learning and nested bundling strategies

Innovation

• Nested bundling menu optimizes seller mechanism
• Buyer learns vertical Gaussian signal comonotonically
• Higher-tier goods receive greater logarithmic variance learning