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

Robert A. Van Gorder and Michael Caputo

Journal of Economic Dynamics and Control, 2010, vol. 34, issue 6, 1123-1139

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.

Keywords: Stackelberg; duopoly; Envelope; theorems; Differential; games; Open-loop; information; structure (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:34:y:2010:i:6:p:1123-1139

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