Non-Linear Strategies in a Linear Quadratic Differential Game

University of Birmingham Economics Working Paper No. 05-05R

31 Pages Posted: 1 Feb 2005

See all articles by Colin Rowat

Colin Rowat

University of Birmingham - Department of Economics

Date Written: January 21, 2006

Abstract

We study non-linear Markov perfect equilibria in a two agent linear quadratic differential game. In contrast to the literature owing to Tsutsui and Mino (1990), we do not associate endogenous subsets of the state space with candidate solutions. Instead, we address the problem of unbounded-below value functions over infinite horizons by use of the 'catching up optimality' criterion. We present sufficiency conditions for existence based on results in Dockner, Jorgenson, Long and Sorger (2000). Applying these to our model yields the familiar linear solution as well as a condition under which a continuum of non-linear solutions exist. As this condition is relaxed when agents are more patient, and allows more efficient steady states, it resembles a Folk Theorem for differential games.

Keywords: Differential game, non-linear strategies, catching up optimal, Folk Theorem

JEL Classification: C61, C73, H41, Q00

Suggested Citation

Rowat, Colin, Non-Linear Strategies in a Linear Quadratic Differential Game (January 21, 2006). University of Birmingham Economics Working Paper No. 05-05R. Available at SSRN: https://ssrn.com/abstract=658061 or http://dx.doi.org/10.2139/ssrn.658061

Colin Rowat (Contact Author)

University of Birmingham - Department of Economics ( email )

Economics Department
Birmingham, B15 2TT
United Kingdom
+44 121 414 3754 (Phone)
+44 121 414 7377 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
127
Abstract Views
1,206
rank
220,612
PlumX Metrics