The local stability of an open-loop Nash equilibrium in a finite horizon differential game

Leonard Cheng*, David Hart

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)

3 Citations (Scopus)

Abstract

We propose a finite time differential game as a model for some economic processes and derive conditions for the Nash equilibrium solution to be locally asymptotically stable. We adopt the traditional 'Cournot-reaction function' notion of stability, which in our (continuous time) model becomes a function-to-function, or trajectory-to-trajectory, mapping. The conditions for stability seem to make economic sense. The equilibrium is less stable if the interaction terms in each period are large, if the game has a long duration, and if the discount rate is small.

Original languageEnglish
Pages (from-to)139-147
Number of pages9
JournalJournal of Mathematical Economics
Volume12
Issue number2
DOIs
Publication statusPublished - 1 Jan 1983
Externally publishedYes

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