The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games
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.
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- 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.
- 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, A.M. & Withagen, C.A.A.M. & de Zeeuw, A.J., 1996. "Strong Time-Consistency in the Cartel-versus-Fringe Model," Discussion Paper 1996-22, Tilburg University, Center for Economic Research.
- Groot, F. & Withagen, C.A.A.M. & de Zeeuw, A.J., 2003. "Strong time-consistency in the cartel-versus-fringe model," Other publications TiSEM 5ba46a2e-d763-4a8c-939b-3, Tilburg University, School of Economics and Management.
- 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, 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.
- 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.
- 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.
- 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.
- 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, June.
- Engwerda, J.C., 2000. "Feedback Nash equilibria in the scalar infinite horizon LQ-Game," Other publications TiSEM 58ccf964-4ca1-4d67-9a68-a, Tilburg University, School of Economics and Management.
- 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.
- Daniel Cohen & Philippe Michel, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," Review of Economic Studies, Oxford University Press, vol. 55(2), pages 263-274.
- 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.
- 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.
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