We propose a discrete-time exchange economy evolutionary model with two groups of agents. In our setting the definition of equilibrium depends also on agents’ population shares, which affect the market clearing conditions. We prove that, despite such difference with the classical Walrasian framework, for all economies and population shares there exists at least one equilibrium, and we show that for all population shares, generically in the set of the economies, equilibria are finite and regular. We then introduce the dynamic law governing the evolution of the population shares, and we investigate the existence and the stability of the resulting stationary equilibria. We assume that the reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is described via a generic bell-shaped map, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts in the agents’ consumption choices, and in the groups’ attractiveness and population shares.

中文翻译：

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具有两组主体的一般平衡进化模型，产生时尚周期动力学

我们提出了具有两组主体的离散时间交换经济演化模型。在我们的设置中，均衡的定义还取决于代理商的人口份额，这会影响市场清算条件。我们证明，尽管与经典的Walrasian框架存在这种差异，但对于所有经济体和人口份额，至少存在一个均衡，并且我们证明，对于所有人口份额（通常在一组经济体中），均衡是有限且规则的。然后，我们介绍了控制人口份额演变的动态定律，并研究了所得静态均衡的存在性和稳定性。我们假设一个群体的繁殖水平与其吸引力程度有关，这取决于社会知名度，由该组中代理商的消费选择确定。通过通用的钟形图来描述组的吸引力，对于低可见性级别，该组的吸引力增加，但是由于拥塞效应，当该组的可见性超过给定阈值时，其吸引力减小。该模型能够再现典型的时尚周期的动态行为，在代理商的消费选择，群体的吸引力和人口份额中呈现出繁荣与萧条。