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

TL;DR

This paper explores how computational limitations of AI agents can lead to trade and market dynamics that differ from classic economic theories, showing that computational power differences can induce trade and instability.

Contribution

It introduces a computational game-theoretic model demonstrating that similar computational power among AI agents can prevent equilibrium, leading to persistent trade and strategic adjustments.

Findings

Stable no-trade occurs only with slight differences in computational power.

Identical computational power can cause persistent strategic adjustments.

Under-utilization of computational resources can prevent equilibrium in matching pennies.

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.