The turnpike property for dynamic discrete time zero-sum games

Abstract

We consider a class of dynamic discrete-time two-player zero-sum games. We show that for a generic cost function and each initial state, there exists a pair of overtaking equilibria strategies over an infinite horizon. We also establish that for a generic cost function $f$, there exists a pair of stationary equilibria strategies $\left(x_f,y_f\right)$ such that each pair of “approximate” equilibria strategies spends almost all of its time in a small neighborhood of $\left(x_f,y_f\right)$.