How To Do Comparative Dynamics On The Back Of An Envelope For Open-Loop Nash Equilibria In Differential Game Theory
Keywords
comparative dynamics; differential games; open-loop Nash equilibria
Abstract
The primal-dual comparative statics method of Samuelson (1965) and Silberberg (1974) is extended to cover the class of non-autonomous, finite horizon differential games in which a locally differentiable open-loop Nash equilibrium exists. In doing so, not only is a one-line proof of an envelope theorem provided but also the heretofore unknown intrinrsic comparative dynamics of open-loop Nash equilibria are uncovered. The intrinsic comparative dynamics are shown to be contained in a symmetric and negative semidefinite matrix that is subject to constraint. The results are applied to a canonical differential game in capital theory, and the resulting comparative dynamics are given an economic interpretation. Copyright © 2016 John Wiley & Sons, Ltd.
Publication Date
5-1-2017
Publication Title
Optimal Control Applications and Methods
Volume
38
Issue
3
Number of Pages
443-458
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1002/oca.2264
Copyright Status
Unknown
Socpus ID
84978286042 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84978286042
STARS Citation
Caputo, Michael R. and Ling, Chen, "How To Do Comparative Dynamics On The Back Of An Envelope For Open-Loop Nash Equilibria In Differential Game Theory" (2017). Scopus Export 2015-2019. 5876.
https://stars.library.ucf.edu/scopus2015/5876