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)Researchpeer-review

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

Fingerprint

Finite Horizon
Differential Games
Local Stability
Nash Equilibrium
Trajectories
Economics
Trajectory
Continuous-time Model
Discount
Equilibrium Solution
Asymptotically Stable
Game
Term
Interaction
Local stability
Open-loop Nash equilibrium
Finite horizon
Differential games
Model
Economic processes

Cite this

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The local stability of an open-loop Nash equilibrium in a finite horizon differential game. / Cheng, Leonard; Hart, David.

In: Journal of Mathematical Economics, Vol. 12, No. 2, 01.01.1983, p. 139-147.

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

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AU - Hart, David

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N2 - 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.

AB - 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.

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