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

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  • Chen Ling
  • Michael Caputo

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

Suggested Citation

  • Chen Ling & Michael Caputo, 2012. "The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 313-334, September.
    • Handle: RePEc:spr:dyngam:v:2:y:2012:i:3:p:313-334
    DOI: 10.1007/s13235-012-0045-8
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    More about this item

    Keywords

    Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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