Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games
AbstractEnvelope 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 34 (2010)
Issue (Month): 6 (June)
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Web page: http://www.elsevier.com/locate/jedc
Stackelberg duopoly Envelope theorems Differential games Open-loop information structure;
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