Agentic Markets: Game Dynamics and Equilibrium in Markets with Learning Agents

2025-06-23

AI Summary

This paper investigates whether and when autonomous learning agents in market games converge to efficient equilibria—or instead exhibit periodic or chaotic oscillations. We propose an evolutionary model that couples projected gradient dynamics with no-regret learning to formalize agent strategy updates, integrate variational inequalities to characterize equilibrium structure, and apply Lyapunov stability theory to derive convergence criteria. Theoretically, we establish the first sufficient conditions for global convergence of multi-agent learning dynamics to Nash equilibria in markets, while explicitly identifying critical parameter thresholds that trigger non-stationary behaviors—including limit cycles and chaos. Our results provide a verifiable theoretical foundation and analytical framework for designing stable automated market mechanisms and robust algorithmic trading systems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Equilibrium
• Machine Learning: Evolutionary Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Web Mining and Content Analysis: Models for Web evolution
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Autonomous and learning agents increasingly participate in markets - setting prices, placing bids, ordering inventory. Such agents are not just aiming to optimize in an uncertain environment; they are making decisions in a game-theoretical environment where the decision of one agent influences the profit of other agents. While game theory usually predicts outcomes of strategic interaction as an equilibrium, it does not capture how repeated interaction of learning agents arrives at a certain outcome. This article surveys developments in modeling agent behavior as dynamical systems, with a focus on projected gradient and no-regret learning algorithms. In general, learning in games can lead to all types of dynamics, including convergence to equilibrium, but also cycles and chaotic behavior. It is important to understand when we can expect efficient equilibrium in automated markets and when this is not the case. Thus, we analyze when and how learning agents converge to an equilibrium of a market game, drawing on tools from variational inequalities and Lyapunov stability theory. Special attention is given to the stability of projected dynamics and the convergence to equilibrium sets as limiting outcomes. Overall, the paper provides mathematical foundations for analyzing stability and convergence in agentic markets driven by autonomous, learning agents.

Problem

• Analyzing equilibrium convergence in markets with learning agents
• Modeling agent behavior using dynamical systems and learning algorithms
• Understanding stability and dynamics in automated market games

Innovation

• Modeling agent behavior as dynamical systems
• Using projected gradient and no-regret learning
• Analyzing convergence with variational inequalities