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

    Authors

    R. A. Van Gorder;M. R. Caputo

    Comments

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    Abbreviated Journal Title

    J. Econ. Dyn. Control

    Keywords

    Stackelberg duopoly; Envelope theorems; Differential games; Open-loop; information structure; INVESTMENT; Economics

    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. (C) 2010 Elsevier B.V. All rights reserved.

    Journal Title

    Journal of Economic Dynamics & Control

    Volume

    34

    Issue/Number

    6

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    1123

    Last Page

    1139

    WOS Identifier

    WOS:000277805000008

    ISSN

    0165-1889

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