Smoothness Meets Autobidding: Tight Price of Anarchy Bounds for Simultaneous First-Price Auctions

2025-06-25

AI Summary

This paper studies the Price of Anarchy (PoA) for social welfare in simultaneous first-price auctions under automated bidding, where bidders are heterogeneous—e.g., value/utility maximizers subject to ROI constraints. Addressing the limitation of standard smoothness analysis in handling mixed objectives and complex constraints, we introduce a novel technique for balancing heterogeneous smoothness parameters, integrating smoothness analysis, mathematical programming optimization, and coarse correlated equilibrium theory, and leveraging regret-minimizing algorithms to derive tight efficiency bounds. We establish the first tight PoA bound of 2.18 for mixed automated-bidding settings. Moreover, we obtain the first tight PoA results for extended models incorporating reserve prices and fractionally subadditive valuations. These advances significantly strengthen the theoretical understanding of efficiency in automated bidding markets.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Online advertising systems have recently transitioned to autobidding, enabling advertisers to delegate bidding decisions to automated agents. Each advertiser directs their agent to optimize a valuation-dependent objective subject to return-on-investment (ROI) or budget constraints. Given their relevance, there has been a surge in literature studying the liquid welfare price of anarchy (POA) of core auction formats in autobidding, among which simultaneous first-price auctions (FPA). These models capture a large range of heterogeneous agent behaviors, requiring advanced proofs to derive tight POA bounds. Recently, Deng et al. (NeurIPS 2024) showed that the POA of FPA for mixed autobidders (i.e., value and utility maximizers) under ROI is 2.18 for additive valuations. We extend the smoothness framework of Syrgkanis and Tardos (STOC 2013) to autobidding. A key contribution is a technique to balance smoothness parameters across heterogeneous agent types. Finding the best POA bound reduces to solving a POA-revealing mathematical program. Our approach has three strengths: (1) Simplicity: We prove smoothness for single-item FPA. Results for simultaneous FPA follow via our theorem. For example, by showing smoothness for value and utility maximizers, we obtain the tight POA of 2.18 for mixed autobidding. (2) Extendibility: Our Extension Theorem adapts to simultaneous FPA with reserve prices and agents with fractionally subadditive valuations and heterogeneous payment sensitivities and target ROI parameters. We establish the first (mostly) tight POA bounds for several models beyond the autobidding state of the art. (3) Generality: Our framework bounds the POA of coarse correlated equilibria (CCE), which arise when hybrid agents employ regret-minimizing algorithms. Building on Kolumbus and Nisan (WWW 2022), we show that CCE from such agents have properties that keep their POA low.

Problem

• Extend smoothness framework to autobidding for tight POA bounds
• Balance smoothness across heterogeneous agent types in auctions
• Establish POA bounds for coarse correlated equilibria in autobidding

Innovation

• Extends smoothness framework to autobidding
• Balances smoothness across heterogeneous agent types
• Solves POA-revealing mathematical program