The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games

    Authors

    M. R. Caputo

    Comments

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    Abbreviated Journal Title

    Games Econ. Behav.

    Keywords

    envelope theorem; differential games; Nash equilibria; OPEN-LOOP; COMPARATIVE STATICS; DYNAMIC GAME; OLIGOPOLY; Economics

    Abstract

    Envelope theorems are established for a ubiquitous class of finite horizon differential games. The theorems cover open-loop and feedback information patterns in which the corresponding Nash equilibria are locally differentiable with respect to the parameters of the game. Their relationship with extant envelope results is discussed and an application of them to a generalized capital accumulation game is provided. An important implication of the theorems is that, in general, the archetypal economic interpretation of the costate vector, namely, as the shadow value of the state vector along the Nash equilibrium, is valid for feedback Nash equilibria, but not for open-loop Nash equilibria. (C) 2007 Elsevier Inc. All rights reserved.

    Journal Title

    Games and Economic Behavior

    Volume

    61

    Issue/Number

    2

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    198

    Last Page

    224

    WOS Identifier

    WOS:000250904700002

    ISSN

    0899-8256

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