The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games
Abbreviated Journal Title
Dyn. Games Appl.
Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria; POLICY; Mathematics, Interdisciplinary Applications
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.
Dynamic Games and Applications
"The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games" (2012). Faculty Bibliography 2010s. 2945.