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

Chen Ling and Michael Caputo

Dynamic Games and Applications, 2012, vol. 2, issue 3, 313-334

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. Copyright Springer Science+Business Media, LLC 2012

Keywords: Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria (search for similar items in EconPapers)
Date: 2012
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Working Paper: The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games (2011)
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DOI: 10.1007/s13235-012-0045-8

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