This paper presents a model of capital accumulation for a large number of heterogeneous producer–consumer agents in an exchange space in which interactions depend on agents’ positions. Agents in the exchange space are subject to both attractive and repulsive forces: exchanges drive agents closer, but crowd out more distant agents. The formalism used in this paper was developed earlier by the authors and is based on statistical field theory. It allows the analytical treatment of economic models with an arbitrary number of agents, while preserving the system’s interactions and microeconomic features of the individual level. Our results show that the dynamics of capital accumulation and the agents’ positions in the exchange space are correlated. Interactions in the exchange space induce phases within the system that depend on the relative strength of the repulsive force. When the repulsive force is strong, the system is in a phase of regulated exchanges. An initial central position both favours and fastens capital accumulation in average, and high levels of initial capital drive agents towards the centre. Yet, this phase displays mild competition and a broad-based although slow improvement in exchange terms. In this phase, random shocks can redistribute capital and initiate a virtuous circle of capital accumulation. When the repulsive force is low, a phase of deregulated exchanges emerges, in which capital distribution is less homogeneous and competition among agents harshens. Increased mobility accelerates capital accumulation for high initial capital producers, whereas low initial capital producers are now evicted from the exchange space as their prices and revenues deteriorate. Thus, a threshold effect appears. Above a certain level of initial capital, agents benefit from and remain in a central position. Below this level, they remain at the periphery of the exchange space.

本文提出了一个交换空间中大量异质生产者-消费者代理的资本积累模型，其中交互取决于代理的位置。交换空间中的智能体同时受到吸引力和排斥力的影响：交换使智能体更靠近，但会排挤距离更远的智能体。本文中使用的形式主义是作者较早开发的，基于统计场论。它允许对具有任意数量代理的经济模型进行分析处理，同时保留系统的相互作用和个体层面的微观经济特征。我们的结果表明，资本积累的动态与代理人在交换空间中的位置是相关的。交换空间中的相互作用会在系统内引起依赖于排斥力相对强度的阶段。当排斥力很强时，系统处于有规律的交换阶段。初始中心位置既有利于并加速了平均资本积累，而高水平的初始资本则将代理人推向中心。然而，这一阶段表现出温和的竞争和广泛的，但在交换方面的缓慢改善。在这个阶段，随机冲击可以重新分配资本并启动资本积累的良性循环。当排斥力较低时，就会出现一个放松管制的交易阶段，其中资本分配不那么同质化，代理人之间的竞争更加激烈。增加的流动性加速了高初始资本生产者的资本积累，而低初始资本的生产者现在随着价格和收入的恶化而被逐出交易空间。因此，出现了阈值效应。超过一定水平的初始资本，代理商受益并保持在中心地位。在这个水平之下，他们仍然处于交换空间的外围。