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

    Authors

    C. Ling;M. R. Caputo

    Comments

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    Abbreviated Journal Title

    Dyn. Games Appl.

    Keywords

    Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria; POLICY; Mathematics, Interdisciplinary Applications

    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.

    Journal Title

    Dynamic Games and Applications

    Volume

    2

    Issue/Number

    3

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    313

    Last Page

    334

    WOS Identifier

    WOS:000328610600004

    ISSN

    2153-0785

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