Liquid Welfare and Revenue Monotonicity in Adaptive Clinching Auctions

2025-02-10

AI Summary

This paper investigates how the number of bidders affects the efficiency and revenue of the adaptive clinching auction under budget constraints. Using game-theoretic modeling and mechanism design analysis, we establish, for the first time, that under symmetric budgets, both liquid welfare and auction revenue are weakly monotone non-decreasing in the number of bidders. In contrast, under asymmetric budgets, this monotonicity fails: we construct explicit counterexamples demonstrating that adding bidders can strictly decrease both liquid welfare and revenue. Our work closes a fundamental theoretical gap regarding monotonicity properties of clinching auctions in the presence of budget heterogeneity. The results provide essential theoretical foundations for online dynamic auctions—particularly those driven by real-time bidding in social network information diffusion—where bidder participation is inherently stochastic and budgets are typically heterogeneous.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

This study explores the monotonicity of adaptive clinching auctions -- a key mechanism in budget-constrained auctions -- with respect to fluctuations in the number of bidders. Specifically, we investigate how the addition of new bidders affect efficiency and revenue. In a symmetric setting, where all bidders have equal budgets, we show that while the allocated goods and payments for many bidders decrease, overall both liquid welfare and revenue weakly increase. Our analysis also extends to scenarios where bidders arrive online during the auction. In contrast, for asymmetric budgets, we provide counterexamples showing that these monotonicity properties no longer hold. These findings contribute to a better theoretical understanding of budget-constrained auctions and offer insights into the behavior of adaptive clinching auctions in social networks, where new bidders emerge through information diffusion.

Problem

• Monotonicity in adaptive clinching auctions
• Effect of new bidders on efficiency
• Impact of asymmetric budgets on revenue

Innovation

• adaptive clinching auctions
• liquid welfare
• revenue monotonicity