Complex Dynamics in Autobidding Systems

TL;DR

This paper investigates the complex and often unpredictable dynamics of autobidding systems in ad auctions, revealing phenomena like bi-stability and periodicity, and demonstrating their ability to simulate logical operations.

Contribution

It provides the first comprehensive analysis of autobidding dynamics, combining empirical observations with theoretical models to uncover complex behaviors and their implications.

Findings

Autobidding systems exhibit bi-stability, periodic orbits, and quasi-periodicity.

Market structure influences the dynamical behavior of autobidders.

Autobidders can simulate linear dynamical systems and boolean logic gates.

Abstract

It has become the default in markets such as ad auctions for participants to bid in an auction through automated bidding agents (autobidders) which adjust bids over time to satisfy return-over-spend constraints. Despite the prominence of such systems for the internet economy, their resulting dynamical behavior is still not well understood. Although one might hope that such relatively simple systems would typically converge to the equilibria of their underlying auctions, we provide a plethora of results that show the emergence of complex behavior, such as bi-stability, periodic orbits and quasi periodicity. We empirically observe how the market structure (expressed as motifs) qualitatively affects the behavior of the dynamics. We complement it with theoretical results showing that autobidding systems can simulate both linear dynamical systems as well logical boolean gates.