Monotonic extensions on economic domains
Monotonic extensions on economic domains
复制标题
经济领域的单调扩展
DOI：
10.1007/s100580050024
复制
发表时间：
1999
影响因子：
0.7
通讯作者：
W. Thomson
中科院分区：
文献类型：
--
作者：
W. Thomson
“单调性”的性质是必要的，而且在许多情况下是充分的，解决方案是纳什可实现的(Maskin 1977)。在这篇文章中，我们遵循Sen(1995)，通过确定一个解必须被放大以满足性质的最小方法来评估它可能不是单调性的程度。我们建立了一个与解族成员的极小单调扩张的交集和并集有关的一般结果。然后，我们计算了几种解决方案在不同背景下的最小单调扩展，例如具有个人天赋或社会天赋的古典交换经济，具有公共产品的经济，以及偏好为单峰型的单一商品经济。对于一些例子来说，恢复单调性几乎不需要什么，但对于另一些例子来说，所需的扩大是相当大的，以至于必须完全放弃解决方案中所包含的分配目标。
The property of “monotonicity” is necessary, and in many contexts, sufficient, for a solution to be Nash implementable (Maskin 1977). In this paper, we follow Sen (1995) and evaluate the extent to which a solution may fail monotonicity by identifying the minimal way in which it has to be enlarged so as to satisfy the property. We establish a general result relating the “minimal monotonic extensions” of the intersection and the union of a family of solutions to the minimal monotonic extensions of the members of the family. We then calculate the minimal monotonic extensions of several solutions in a variety of contexts, such as classical exchange economies, with either individual endowments or a social endowment, economies with public goods, and one-commodity economies in which preferences are single-peaked. For some of the examples, very little is needed to recover monotonicity, but for others, the required enlargement is quite considerable, to the point that the distributional objective embodied in the solution has to be given up altogether.