We study exchange economies where the preference relation of each consumer depends also on the consumptions of the other consumers. In the setting of economies with a finite number \(n\ge 2\) of consumers and non-ordered and discontinuous preferences, we give sufficient and necessary conditions for the existence of alpha-core allocations in the sense of Yannelis (Equilibrium theory in infinite dimensional spaces, 102–123, 1991). The result has been obtained by means of the Ky Fan minimax inequality.

中文翻译：

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在具有无序和不连​​续偏好的经济体中存在阿尔法核心分配

我们研究交换经济，其中每个消费者的偏好关系也取决于其他消费者的消费。在具有有限数量\(n\ge 2\)消费者和非有序和不连续偏好的经济体设置中，我们给出了 Yannelis 意义上的 alpha 核心分配存在的充分和必要条件（均衡理论无限维空间，102-123，1991）。结果是通过 Ky Fan 极小极大不等式获得的。