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.

翻译：随着人工智能的近期发展，在经济活动中采用AI智能体已愈发普遍。本文探讨了在涉及产品/服务交易的经济博弈中，包括人类智能体与AI智能体在内的各类智能体的经济行为，以及这一多智能体经济中的均衡状态。我们基于马尔可夫链平稳分布模型推导出一系列均衡结果及其对应条件。我们模型的一个显著特点是，我们关注经济活动产生的长期效用而非短期收益。对于包含两个智能体的模型，我们完整刻画了所有可能的经济均衡及其条件。有趣的是，我们发现：除非每个智能体通过购买对方产品/服务所能获得的边际效用至少能翻倍（而非仅仅增加），否则在任何经济均衡中都不会发生购买对方产品/服务的行为。我们进一步将结论推广至三个及更多智能体的情形，刻画了更多类型的经济均衡。研究发现，在某些均衡状态下，“能力更强”的AI智能体对“能力较弱”的智能体贡献的效用为零。