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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

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File URL: http://hdl.handle.net/10.1007/s13235-012-0045-8
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Bibliographic Info

Article provided by Springer in its journal Dynamic Games and Applications.

Volume (Year): 2 (2012)
Issue (Month): 3 (September)
Pages: 313-334

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Handle: RePEc:spr:dyngam:v:2:y:2012:i:3:p:313-334

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Web page: http://www.springer.com/economics/journal/13235

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Related research

Keywords: Envelope theorem; Differential games; Open-loop Nash equilibria; Feedback Nash equilibria;

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  1. Groot, F. & Withagen, C.A.A.M. & Zeeuw, A.J. de, 2003. "Strong time-consistency in the cartel-versus-fringe model," Open Access publications from Tilburg University urn:nbn:nl:ui:12-117032, Tilburg University.
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  3. Cohen, Daniel & Michel, Philippe, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," Review of Economic Studies, Wiley Blackwell, vol. 55(2), pages 263-74, April.
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  7. Van Gorder, Robert A. & Caputo, Michael R., 2010. "Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1123-1139, June.
  8. Miller, Marcus & Salmon, Mark, 1985. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," Economic Journal, Royal Economic Society, vol. 95(380a), pages 124-37, Supplemen.
  9. Caputo, Michael R., 2007. "The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 198-224, November.
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