Artificial Superintelligence May be Useless: Equilibria in the Economy of Multiple AI Agents
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
| Scenario | Equilibrium Results | Equilibrium Conditions | Proposition |
|---|---|---|---|
| 1 | No adoption ( ) | always holds | 1 and 6 |
| 2 | Bilateral partial adoption | ||
| ( and ) | and | 2 | |
| 3 | Bilateral full adoption ( ) | and | 5 |
| 4 | Unilateral full adoption | ||
| ( , and | and | 3 |
Multi-Agent Systems
Multi-Agent Systems studies how autonomous agents coordinate, compete, communicate, and learn in shared or interdependent tasks.
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