The Root of Revenue Continuity

2025-07-21

AI Summary

This paper investigates the stability of the seller’s optimal revenue under small perturbations to buyers’ value distributions in multi-item auctions. Using the Wasserstein-1 distance (W_1) to quantify distributional divergence, it establishes the first tight Hölder continuity bound for the revenue function: (ig|sqrt{mathrm{Rev}(X)} - sqrt{mathrm{Rev}(Y)}ig| leq sqrt{W_1(X,Y)}), thereby characterizing revenue robustness to distributional shifts. Theoretically, it shows that when value distributions are close in (W_1), applying a uniform discount to the original optimal mechanism suffices to achieve near-optimal revenue—eliminating the need to recompute complex mechanisms. This result bridges mechanism design and optimal transport theory, yielding a computationally tractable and implementation-friendly foundation for robust auction design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: 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: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In the setup of selling one or more goods, various papers have shown, in various forms and for various purposes, that a small change in the distribution of a buyer's valuations may cause only a small change in the possible revenue that can be extracted. We prove a simple, clean, convenient, and general statement to this effect: let X and Y be random valuations on k additive goods, and let W(X,Y) be the Wasserstein (or "earth mover's") distance between them; then sqrt(Rev(X))-sqrt(Rev(Y)) <= sqrt(W(X,Y)). This further implies that a simple explicit modification of any optimal mechanism for X, namely, "uniform discounting", is guaranteed to be almost optimal for any Y that is close to X in the Wasserstein distance.

Problem

• Study revenue continuity in multi-good auctions
• Quantify revenue change via Wasserstein distance
• Propose near-optimal mechanism for similar valuations

Innovation

• Uses Wasserstein distance for valuation distributions
• Proves revenue continuity with sqrt(Rev) bound
• Proposes uniform discounting for near-optimal mechanisms