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Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games

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Listed author(s):
  • Van Gorder, Robert A.
  • Caputo, Michael R.

Abstract

Envelope theorems are established for locally differentiable Stackelberg equilibria of a general class of finite horizon differential games with an open-loop information structure. It is shown that the follower's envelope results agree in form with those of any player in an open-loop Nash equilibrium, while those of the leader differ. An unanticipated conclusion is that the costate vector of the leader--but not that of the follower--corresponding to the state vector of the differential game may be legitimately interpreted as the shadow value of the state vector for time-inconsistent open-loop Stackelberg equilibria. Surprisingly, the same cannot be said for time-consistent open-loop Stackelberg equilibria.

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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 34 (2010)
Issue (Month): 6 (June)
Pages: 1123-1139

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Handle: RePEc:eee:dyncon:v:34:y:2010:i:6:p:1123-1139
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

Keywords: Stackelberg duopoly Envelope theorems Differential games Open-loop information structure;

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  1. A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
  2. Ely, Jeffrey & Fudenberg, Drew & Levine, David K., 2008. "When is reputation bad?," Games and Economic Behavior, Elsevier, vol. 63(2), pages 498-526, July.
  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. Jorgensen, Steffen & Kort, Peter M. & Van Schijndel, Geert-Jan C. Th., 1989. "Optimal investment, financing, and dividends : A stackelberg differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 339-377, July.
  5. repec:ebl:ecbull:v:12:y:2006:i:12:p:1-9 is not listed on IDEAS
  6. Morgan, John & Vardy, Felix, 2007. "The value of commitment in contests and tournaments when observation is costly," Games and Economic Behavior, Elsevier, vol. 60(2), pages 326-338, August.
  7. Amitrajeet A. Batabyal & Hamid Beladi, 2008. "A Stackelberg Game Model Of Trade In Renewable Resources With Competitive Sellers," World Scientific Book Chapters, in: Dynamic And Stochastic Approaches To The Environment And Economic Development, chapter 7, pages 103-121 World Scientific Publishing Co. Pte. Ltd..
  8. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
  9. Caputo, Michael R., 1992. "Fundamental symmetries and qualitative properties in the adjustment cost model of the firm," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 99-112.
  10. Solan, Eilon & Yariv, Leeat, 2004. "Games with espionage," Games and Economic Behavior, Elsevier, vol. 47(1), pages 172-199, April.
  11. Koji Shimomura & Danyang Xie, 2008. "Advances on Stackelberg open-loop and feedback strategies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 115-133.
  12. Xie, Danyang, 1997. "On Time Inconsistency: A Technical Issue in Stackelberg Differential Games," Journal of Economic Theory, Elsevier, vol. 76(2), pages 412-430, October.
  13. 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, January.
  14. 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.
  15. Cremer, Jacques, & Riordan, Michael H, 1985. "A Sequential Solution to the Public Goods Problem," Econometrica, Econometric Society, vol. 53(1), pages 77-84, January.
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Cited by:

  1. 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.
  2. Steffen Jørgensen, 2011. "Intertemporal Contracting in a Supply Chain," Dynamic Games and Applications, Springer, vol. 1(2), pages 280-300, June.

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