标题： 要不要使用人工智能，要不要购买本地产品：真实价格的数学理论 显示英文标题

标题： To AI or not to AI, to Buy Local or not to Buy Local: A Mathematical Theory of Real Price

摘要： 在过去几十年里，世界经济变得越来越全球化。另一方面，也有一些提倡“购买本地”理念的观点，通过这种方式，人们购买本地生产的商品和服务，而不是远离本地生产的产品。在本文中，我们建立了一种数学理论来确定真实价格，该理论可以决定一个代理在全球和本地消费之间的最优选择，从而实现代理在消费和获得效用之间的最优权衡。我们关于真实价格的理论依赖于与生产者和消费者网络相关的马尔可夫链转移概率矩阵的渐近分析。我们证明了产品或服务的真实价格可以从涉及的马尔可夫链矩阵中确定，并且可能与产品标签价格大相径庭。特别是，我们表明产品和服务的标签价格通常并不“真实”或直接“有用”：给定两个提供相同短期效用的产品，标签价格较低的那个不一定能提供更好的长期效用。这一理论表明，产品和服务的全球性或地方性确实会对客户的消费-效用权衡产生不同的影响。所建立的数学理论可以用来从经济角度确定是否采用某些人工智能（AI）技术。 显示英文摘要

摘要： In the past several decades, the world's economy has become increasingly globalized. On the other hand, there are also ideas advocating the practice of ``buy local'', by which people buy locally produced goods and services rather than those produced farther away. In this paper, we establish a mathematical theory of real price that determines the optimal global versus local spending of an agent which achieves the agent's optimal tradeoff between spending and obtained utility. Our theory of real price depends on the asymptotic analysis of a Markov chain transition probability matrix related to the network of producers and consumers. We show that the real price of a product or service can be determined from the involved Markov chain matrix, and can be dramatically different from the product's label price. In particular, we show that the label prices of products and services are often not ``real'' or directly ``useful'': given two products offering the same myopic utility, the one with lower label price may not necessarily offer better asymptotic utility. This theory shows that the globality or locality of the products and services does have different impacts on the spending-utility tradeoff of a customer. The established mathematical theory of real price can be used to determine whether to adopt or not to adopt certain artificial intelligence (AI) technologies from an economic perspective.