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

TL;DR

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, and derives a range of equilibrium results and their corresponding conditions using a Markov chain stationary distribution based model.

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 (1)

• 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 $A$.

Theorems & Definitions (24)

• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Proposition 4
• proof
• Proposition 5
• proof