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

Socpus ID

84978286042 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84978286042

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