Title

The Envelope Theorem For Locally Differentiable Nash Equilibria Of Finite Horizon Differential Games

Keywords

Differential games; Envelope theorem; Nash equilibria

Abstract

Envelope theorems are established for a ubiquitous class of finite horizon differential games. The theorems cover open-loop and feedback information patterns in which the corresponding Nash equilibria are locally differentiable with respect to the parameters of the game. Their relationship with extant envelope results is discussed and an application of them to a generalized capital accumulation game is provided. An important implication of the theorems is that, in general, the archetypal economic interpretation of the costate vector, namely, as the shadow value of the state vector along the Nash equilibrium, is valid for feedback Nash equilibria, but not for open-loop Nash equilibria. © 2007 Elsevier Inc. All rights reserved.

Publication Date

11-1-2007

Publication Title

Games and Economic Behavior

Volume

61

Issue

2

Number of Pages

198-224

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.geb.2007.01.004

Socpus ID

35148899738 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/35148899738

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