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

  • Micahel Caputo

    ()

    (University of Central Florida, Orlando, FL)

  • Chen Ling

    ()

    (Southwestern University of Finance and Economics, Chengdu, Sichuan, China)

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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File URL: https://www.trc.bus.ucf.edu/cdn/economics/workingpapers/2011-06.pdf
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Paper provided by University of Central Florida, Department of Economics in its series Working Papers with number 2011-06.

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Length: 24 Pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:cfl:wpaper:2011-06
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Web page: http://www.bus.ucf.edu/economics/

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-81029 is not listed on IDEAS
  8. 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.
  9. 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.
  10. 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.
  11. repec:cup:cbooks:9780521637329 is not listed on IDEAS
  12. 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.
  13. repec:dgr:kubcen:199622 is not listed on IDEAS
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