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Non-linear strategies in a linear quadratic differential game

Colin Rowat ()

GE, Growth, Math methods from EconWPA

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. The model presented here is one of atmospheric pollution; the results apply to differential games more generally.

Keywords: differential game; non-linear strategies; catching up optimal; Folk Theorem (search for similar items in EconPapers)
JEL-codes: C61 C73 H41 Q00 (search for similar items in EconPapers)
Date: 2005-02-01
Note: Type of Document - pdf; pages: 31. University of Birmingham Department of Economics Discussion Paper 05-05
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Related works:
Journal Article: Non-linear strategies in a linear quadratic differential game (2007) Downloads
Working Paper: Non-Linear Strategies in a Linear Quadratic Differential Game (2005)
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