Chaos in Autobidding Auctions

2026-02-09

AI Summary

This study investigates whether automated bidding systems exhibit chaotic dynamics over long-term operation. Under unified bid scaling and return-on-investment constraints, the authors construct a dynamic evolution model of auto-bidding agents and rigorously demonstrate, for the first time, that such systems can emulate continuous-time nonlinear systems—exemplified by the Chua circuit—and satisfy the defining properties of chaos, including Li-Yorke chaos, topological transitivity, and sensitivity to initial conditions. By leveraging dynamical systems theory, modular construction techniques, and mirror descent algorithms, the work establishes formal connections between auto-bidding dynamics and classical chaotic models such as the Logistic map and Ricker model. This research transcends prior observations limited to quasiperiodicity, revealing that second-price auto-bidding auctions can generate intrinsically unpredictable, complex chaotic behavior even under simple bidding rules.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• 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
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

As autobidding systems increasingly dominate online advertising auctions, characterizing their long-term dynamical behavior is brought to the fore. In this paper, we examine the dynamics of autobidders who optimize value subject to a return-on-spend (RoS) constraint under uniform bid scaling. Our main set of results show that simple autobidding dynamics can exhibit formally chaotic behavior. This significantly strengthens the recent results of Leme, Piliouras, Schneider, Spendlove, and Zuo (EC'24) that went as far as quasiperiodicity. Our proof proceeds by establishing that autobidding dynamics can simulate -- up to an arbitrarily small error -- a broad class of continuous-time nonlinear dynamical systems. This class contains as a special case Chua's circuit, a classic chaotic system renowned for its iconic double scroll attractor. Our reduction develops several modular gadgets, which we anticipate will find other applications going forward. Moreover, in discrete time, we show that different incarnations of mirror descent can exhibit Li-Yorke chaos, topological transitivity, and sensitivity to initial conditions, connecting along the way those dynamics to classic dynamical systems such as the logistic map and the Ricker population model. Taken together, our results reveal that the long-term behavior of ostensibly simple second-price autobidding auctions can be inherently unpredictable and complex.

Problem

• autobidding
• chaos
• auctions
• dynamical systems
• return-on-spend

Innovation

• chaos
• autobidding
• mirror descent
• Chua's circuit
• nonlinear dynamics