Envelope theorems for arbitrary choice sets

被引：537

作者：

Milgrom, P ^{[1
]}

Segal, I ^{[1
]}

机构：

[1] Stanford Univ, Dept Econ, Stanford, CA 94305 USA

来源：

ECONOMETRICA | 2002年 / 70卷 / 02期

关键词：

envelope theorem; differentiable value function; sensitivity analysis; math programming; mechanism design;

D O I：

10.1111/1468-0262.00296

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left- and right-differentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddle-point problems, problems with parameterized constraints, and optimal stopping problems.

引用

页码：583 / 601

页数：19