### 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 language | English |
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Pages (from-to) | 139-147 |

Number of pages | 9 |

Journal | Journal of Mathematical Economics |

Volume | 12 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1983 |

Externally published | Yes |

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*Journal of Mathematical Economics*, vol. 12, no. 2, pp. 139-147. https://doi.org/10.1016/0304-4068(83)90009-5

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

Research output: Journal Publications › Journal Article (refereed) › Research › peer-review

TY - JOUR

T1 - The local stability of an open-loop Nash equilibrium in a finite horizon differential game

AU - Cheng, Leonard

AU - Hart, David

PY - 1983/1/1

Y1 - 1983/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=48749149349&partnerID=8YFLogxK

U2 - 10.1016/0304-4068(83)90009-5

DO - 10.1016/0304-4068(83)90009-5

M3 - Journal Article (refereed)

VL - 12

SP - 139

EP - 147

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 2

ER -