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Envelope Theorems for Arbitrary Choice Sets (2002)
| Venue: | ECONOMETRICA |
| Citations: | 211 - 8 self |
BibTeX
@ARTICLE{Milgrom02envelopetheorems,
author = {Paul Milgrom and Ilya Segal},
title = { Envelope Theorems for Arbitrary Choice Sets},
journal = {ECONOMETRICA},
year = {2002},
volume = {70},
number = {2},
pages = {583--610}
}
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Abstract
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.
Keyphrases
arbitrary choice set value function standard envelope parameterized constraint sufficient condition continuous optimization problem optimal stopping problem convex programming traditional envelope formula topological structure differentiability point saddle-point problem choice set paper study
