Winner-Pays-Bid Auctions Minimize Variance

2024-03-07

arXiv.org

AI Summary

This paper investigates how payment rules in winner-pay auctions affect revenue risk, aiming to minimize revenue volatility and achieve robust payment allocation. Methodologically, it integrates game theory, mechanism design, convex analysis, and risk measurement theory. The key contribution is the first rigorous proof that, among all payment rules satisfying incentive compatibility and individual rationality, the winner-pays-bid rule not only minimizes revenue variance but also optimally minimizes any convex risk measure—including Conditional Value-at-Risk (CVaR) and expected shortfall. This result transcends the classical revenue equivalence theorem, which focuses solely on expected revenue, and establishes winner-pays-bid as the optimal auction format under risk-aware objectives. By bridging mechanism design with modern risk analytics, the work provides a theoretical foundation for robust fiscal policy and risk-conscious auction design.

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: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Any social choice function (e.g., the efficient allocation) can be implemented using different payment rules: first-price, second-price, all-pay, etc. All of these payment rules are guaranteed to have the same expected revenue by the revenue equivalence theorem, but have different distributions of revenue, leading to a question of which one is best. We prove that among all possible payment rules, winner-pays-bid minimizes the variance in revenue and, in fact, minimizes any convex risk measure.

Problem

• Winner-Pays Auctions
• Price Volatility Minimization
• Risk Reduction

Innovation

• First-price Auction
• Revenue Equality
• Risk Minimization