2002•DIAL (Catholic University of Leuven)Open access

On the selection of one feedback Nash equilibrium in discounted linear-quadratic games

Pierre Cartigny, Philippe Michel

Abstract

We study a selection method for a Nash feedback equilibrium of a one-dimensional linear-quadratic nonzero sum game over an infinite horizon : by introducing a change in the time variable, one obtains an associated game over a finite horizon T > 0 and with free terminal state. This associated game admits a unique solution which converges to a particular Nash feedback equilibrium of the original problem as the horizon T goes to infinity. Key Words. Linear-quadratic games. Nonzero sum differential games. Nash equilibria. Infinite horizon.

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Key concepts: Nash equilibrium, Epsilon-equilibrium, Mathematical economics, Best response, Differential game, Mathematics, Correlated equilibrium, Equilibrium selection