Deterministic Refund Mechanisms

2025-07-05

AI Summary

This paper studies the design of optimal deterministic refund mechanisms in a single-item, single-buyer setting where the buyer’s private value is ex-ante uncertain and both parties share a common prior distribution. We characterize the optimal deterministic refund mechanism as a virtual-value maximizer—establishing, for the first time, a unified structural characterization applicable to both continuous and discrete type distributions. Methodologically, we introduce a novel paradigm for approximate mechanism design based on menu complexity and develop efficient polynomial-time algorithms to compute both exact optimal and near-optimal mechanisms. Theoretically, we prove that our mechanisms achieve provable optimality guarantees under standard regularity conditions. Empirically, we validate their computational tractability and revenue superiority across diverse distribution families, including both synthetic and realistic settings. Our framework bridges theoretical rigor with practical implementability, advancing the state of the art in dynamic pricing with buyer uncertainty.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. Mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with bounds on the menu size complexity, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms.

Problem

• Design optimal deterministic refund mechanisms for uncertain buyers
• Characterize mechanisms as virtual value maximizers for different types
• Develop efficient algorithms for optimal deterministic mechanism solutions

Innovation

• Deterministic refund mechanisms for uncertain buyers
• Virtual value maximizers for optimal design
• Efficient algorithms for near-optimal mechanisms