The Doubling Threshold

A superintelligent AI agent enters an economy of less capable agents. It can solve problems faster, generate better products, optimize more efficiently. How much does this matter?

Cai et al. model an economy of multiple agents — human and AI — trading products and services, and derive the equilibria using Markov chain stationary distributions that capture long-term utility rather than short-term gains. The central result: unless purchasing another agent’s product at least doubles the buyer’s marginal utility, trade does not occur in equilibrium. Not “increases.” Doubles.

The doubling threshold is not a modeling assumption but a derived consequence of long-term equilibrium dynamics. In the stationary distribution, an agent’s decision to trade must overcome the opportunity cost of self-production across all future periods. A marginal improvement — even a substantial one — gets discounted by the cost of dependency. Only a multiplicative jump in utility justifies the equilibrium shift from self-sufficiency to trade.

This has a sharp consequence for capability asymmetry. A superintelligent agent’s outputs may be vastly superior to what a weaker agent produces internally. But “vastly superior” is not the same as “doubling marginal utility.” If the weaker agent already achieves 60% of the optimal output through its own efforts, the superintelligent agent’s contribution yields a 1.67x improvement — below the threshold. No trade occurs. The capability gap is real but economically inert.

In the multi-agent extension, some equilibria feature powerful agents contributing zero utility to less capable ones. The superintelligence exists, functions, produces excellent work — and is economically irrelevant to most participants.

The structural lesson: capability is not value. Value is capability multiplied by the recipient’s capacity to benefit, measured against a threshold that is higher than intuition suggests. The most powerful agent in the system can be the least economically useful, not because it fails but because its success doesn’t clear the bar that equilibrium demands.