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

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  • 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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Cited by:

  1. 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.
  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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