A note on discontinuous value functions and strategies in afine-quadratic differential games

Paper number: 95/14

Paper date: August 1995

Year: 1995

Paper Category: Discussion Paper

Authors

Henrick Jensen
University of Copenhagen*

Ben Lockwood
University of Exeter and CEPR**

Abstract

We present an economic example of an affine-quadratic differential game where in Markov-perfect Nash equilibrium, the value function of a player is discontinuous in the model's parameters, implying that the strategy of that player is also discontinuous, even though the data of the game (state equation and pay-offs) are continuous in the parameters. Sufficient conditions ruling out such discontinuities are presented for the general scalar case.

JEL Classification number: C73.
Keywords: Affine-quadratic differential games, Markov-perfect equilibrium, Discontinuous strategies.

*Corresponding author. Mailing address: Institute of Economics, University of Copenhagen, Studiestraede 6, DK-1455 Copenhagen K, Denmark. Phone: + 45 35 32 30 43; Fax: + 45 35 32 30 00; E-mail: henrikj@pc.ibt.dk
**Mailing address: Department of Economics, University of Exeter, Exeter, EX4 4RJ, England.