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


  • Van Gorder, Robert A.
  • Caputo, Michael R.


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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:34:y:2010:i:6:p:1123-1139

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    References listed on IDEAS

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    Cited by:

    1. repec:eee:apmaco:v:320:y:2018:i:c:p:240-250 is not listed on IDEAS
    2. 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.
    3. 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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