Will AI Trade? A Computational Inversion of the No-Trade Theorem

2025-12-16

AI Summary

This paper challenges the classical no-trade theorem by examining whether AI agents with common priors and bounded computational capacity can still engage in trade. Method: We model bounded rationality using an extensive-form game framework, incorporating strategic resource throttling and constraints on strategy complexity, and analyze dynamics via the Matching Pennies game. Contribution/Results: Under perfectly symmetric computational capacity, the Nash equilibrium collapses, inducing persistent strategy oscillation and endogenous trade; conversely, even slight computational asymmetry stabilizes behavior and suppresses trade. We identify the counterintuitive paradigm that “computational asymmetry promotes no-trade, whereas symmetry induces trade,” formally demonstrating that computational symmetry can violate equilibrium existence. Moreover, when agents are permitted to strategically idle computational resources, equilibria vanish entirely, markedly amplifying market dynamism and unpredictability. This work establishes computational symmetry—not just information or preferences—as a critical determinant of trade feasibility and equilibrium stability.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Humans and AI: Other Foundations of Human Computation & AI

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Social Networks and Social Media: Computational social science
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Classic no-trade theorems attribute trade to heterogeneous beliefs. We re-examine this conclusion for AI agents, asking if trade can arise from computational limitations, under common beliefs. We model agents' bounded computational rationality within an unfolding game framework, where computational power determines the complexity of its strategy. Our central finding inverts the classic paradigm: a stable no-trade outcome (Nash equilibrium) is reached only when "almost rational" agents have slightly different computational power. Paradoxically, when agents possess identical power, they may fail to converge to equilibrium, resulting in persistent strategic adjustments that constitute a form of trade. This instability is exacerbated if agents can strategically under-utilize their computational resources, which eliminates any chance of equilibrium in Matching Pennies scenarios. Our results suggest that the inherent computational limitations of AI agents can lead to situations where equilibrium is not reached, creating a more lively and unpredictable trade environment than traditional models would predict.

Problem

• Examining if computational limitations cause trade among AI agents
• Modeling bounded rationality in AI agents within unfolding game framework
• Finding that identical computational power prevents equilibrium, enabling persistent trade

Innovation

• Modeling bounded computational rationality in unfolding games
• Trade arises from identical computational power causing instability
• Strategic under-utilization of resources eliminates equilibrium chances