In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

在本文中，我们研究了交换经济中代理人之间的资源公平再分配问题 á la Shitovitz (Econometrica 41:467–501, 1973)，代理人的度量空间既有原子部分，也有无原子部分。我们遵循 Aubin 的思想（博弈经济理论的数学方法。北荷兰，阿姆斯特丹，纽约，牛津，1979 年）允许个人部分参与联盟，这会导致普通联盟的集合扩大到所谓的模糊或广义联盟。我们提出了一个公平的概念，除了效率之外，它不会对模糊联盟产生嫉妒，并且充分表征了竞争均衡和 Aubin 核心分配。