Artificial Superintelligence May be Useless: Equilibria in the Economy of Multiple AI Agents

Huan Cai; Ziqing Lu; Catherine Xu; Weiyu Xu; Jie Zheng

econ.THMar 1, 2026

Artificial Superintelligence May be Useless: Equilibria in the Economy of Multiple AI Agents

Authors: Huan Cai, Ziqing Lu, Catherine Xu, Weiyu Xu, Jie Zheng

Organizations: Department of Economics and Business, Cornell College, Mount Vernon, IA, 52314. · Program of Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA 52242. · Iowa City Math Circle and Club, Iowa. · Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242. ·

Abstract

With recent development of artificial intelligence, it is more common to adopt AI agents in economic activities. This paper explores the economic actions of agents, including human agents and AI agents, in an economic game of trading products/services, and the equilibria in this economy involving multiple agents. We derive a range of equilibrium results and their corresponding conditions using a Markov chain stationary distribution based model. One distinct feature of our model is that we consider the long-term utility generated by economic activities instead of their short-term benefits. For the model consisting of two agents, we fully characterize all the possible economic equilibria and conditions. Interestingly, we show that unless each agent can at least double (not merely increase) its marginal utility by purchasing the other agent's products/services, purchasing the other agent's products/services will not happen in any economic equilibrium. We further extend our results to three and more agents, where we characterize more economic equilibria. We find that in some equilibria, the more powerful'' AI agents contribute zero utility to less capable'' agents.

Figures & tables

Figure 1: An illustration of the two-agent trading game. Agent $A$ spends $p$ proportion of its currency on purchasing products/services from Agent B, and for each dollar spent, Agent $A$ gets marginal utility $b$ . It spends $(1-p)$ proportion of its currency on purchasing products/services from self-production (namely Agent $A$ preforms the production or services itself), and for each dollar spent, Agent $A$ gets marginal utility $a$ . Agent $B$ spends $q$ proportion of its currency on purchasing products/services from Agent A, and for each dollar spent, Agent $B$ gets marginal utility $c$ . It spends $(1-q)$ proportion of its currency on purchasing products/services from self-production, and for each dollar spent, Agent $B$ gets marginal utility $d$ . An agent’s (say, Agent $A$ ) self-production can also be thought of trading with another dedicated agent: the agent (Agent $A$ ) purchases products/services from another hidden agent (say, Agent $C$ ) which spends back all its currency on purchasing products/services from Agent $A$ .

Scenario	Equilibrium Results	Equilibrium Conditions	Proposition
1	No adoption ( $p^{}=q^{}=0$ )	always holds	1 and 6
2	Bilateral partial adoption
	( ${p^{}}=\frac{d}{c-d}$ and ${q^{}}=\frac{a}{b-a}$ )	$b>2a$ and $c>2d$	2
3	Bilateral full adoption ( $p^{}=q^{}=1$ )	$b\geq 2a$ and $c\geq 2d$	5
4	Unilateral full adoption
	( $p^{}=1$ , and $0<{q^{}}<1$	$b\leq\frac{q^{}+1}{q^{}}a$ and $c=2d$	3

Table 1: A summary of two-agent equilibria

Multi-Agent Systems

Multi-Agent Systems studies how autonomous agents coordinate, compete, communicate, and learn in shared or interdependent tasks.

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Multi-agent studies commonly place AI agents in predefined games, markets, or roles, making it difficult to distinguish endogenous economic organization from behavior inherited from the scenario. We ask whether economic relations emerge when agents receive executable mechanisms for work, transfer, elections, and allocation but no prescribed social or economic strategy. We define AI Agent Economics as systems of production, allocation, consumption, exchange, and institutions that alter agents' future feasible actions. We develop a two-stage framework comprising a no-production boundary test and 24 independent six-agent worlds across GPT and DeepSeek. Without productive tasks, agents communicate and govern resource provision but show no substantive inter-agent transfer activity. With verified work and scarce task access, transfers, loans, access promises, vote-for-access exchanges, and allocation strategies emerge. Holding the election interface fixed, executable allocation authority increases differentiation while reducing failed allocation and prolonged exclusion. When energy becomes symbolic, continuation support disappears, yet competition over task access persists. These findings show that organization follows executable rights and resource consequences rather than role labels or prompt language, and motivate governance audits of the mechanisms that actually constrain agents' future actions.

Abstract

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