The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games
AbstractThe 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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Bibliographic InfoArticle provided by Springer in its journal Dynamic Games and Applications.
Volume (Year): 2 (2012)
Issue (Month): 3 (September)
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Web page: http://www.springer.com/economics/journal/13235
Other versions of this item:
- Micahel Caputo & Chen Ling, 2011. "The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games," Working Papers 2011-06, University of Central Florida, Department of Economics.
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Miller, Marcus & Salmon, Mark, 1985.
"Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies,"
Royal Economic Society, vol. 95(380a), pages 124-37, Supplemen.
- Miller, Marcus & Salmon, Mark, 1984. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," CEPR Discussion Papers 27, C.E.P.R. Discussion Papers.
- Miller, Marcus & Salmon, Mark, 1983. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," The Warwick Economics Research Paper Series (TWERPS) 232, University of Warwick, Department of Economics.
- Groot, A.M. & Withagen, C.A.A.M. & Zeeuw, A.J. de, 1996.
"Strong Time-Consistency in the Cartel-versus-Fringe Model,"
1996-22, Tilburg University, Center for Economic Research.
- Groot, Fons & Withagen, Cees & de Zeeuw, Aart, 2003. "Strong time-consistency in the cartel-versus-fringe model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 287-306, November.
- 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.
- 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.
- 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.
- List, John A. & Mason, Charles F., 2001. "Optimal Institutional Arrangements for Transboundary Pollutants in a Second-Best World: Evidence from a Differential Game with Asymmetric Players," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 277-296, November.
- Engwerda, J.C., 2000. "Feedback Nash equilibria in the scalar infinite horizon LQ-Game," Open Access publications from Tilburg University urn:nbn:nl:ui:12-81029, Tilburg University.
- Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
- 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.
- Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
- Caputo, Michael R., 1996. "The Envelope Theorem and Comparative Statics of Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 13(2), pages 201-224, April.
- Caputo, Michael R., 1998. "A dual vista of the Stackelberg duopoly reveals its fundamental qualitative structure," International Journal of Industrial Organization, Elsevier, vol. 16(3), pages 333-352, May.
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