The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games

Michael Caputo and Chen Ling

No 2011-06, Working Papers from University of Central Florida, Department of Economics

Abstract: The envelope theorem is extended to cover the class of discounted and autonomous infinite horizon differential games that possess locally differentiable Nash equilibria. The theorems cover open-loop and feedback information structures and are applied to an analytically solvable linear-quadratic game. The linear-quadratic structure permits additional insight into the theorems that is not available in the general case. With open-loop information, for example, the costate variable is shown to uniformly overstate the shadow value of the state variable, but the growth rates of the two are identical.

Keywords: Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria (search for similar items in EconPapers)
JEL-codes: C72 C73 L13 (search for similar items in EconPapers)
Pages: 24 Pages
Date: 2011-08
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Related works:
Journal Article: The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games (2012)
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