Existence of Optimal Mechanisms for Selling Multiple Goods: An Elementary Proof

2026-01-04

arXiv.org

AI Summary

This work establishes the existence of a revenue-maximizing mechanism in multi-good, multi-parameter settings under remarkably weak distributional assumptions—specifically, when buyers’ valuation distributions possess only finite expectations. Departing from prior approaches that rely on strong regularity conditions or sophisticated functional-analytic machinery, the proof employs a constructive method grounded in elementary tools from measure theory and optimization theory within the classical mechanism design framework. The resulting argument is both concise and self-contained, significantly relaxing the standard assumptions required by existing literature. By doing so, this study provides a more robust theoretical foundation for the existence of optimal auctions in multi-good environments, broadening the scope of applicability of mechanism design theory to a substantially wider class of valuation distributions.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements

Abstract

We provide an elementary proof that revenue-maximizing mechanisms exist in multi-parameter settings whenever the distribution of valuations has finite expectation.

Problem

• optimal mechanisms
• multiple goods
• revenue maximization
• multi-parameter settings
• valuation distribution

Innovation

• optimal mechanism
• multi-parameter settings
• revenue maximization
• elementary proof
• finite expectation