Abstract and Applied Analysis
Volume 4 (1999), Issue 1, Pages 21-48
doi:10.1155/S1085337599000020

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 (xf,yf) such that each pair of “approximate” equilibria strategies spends almost all of its time in a small neighborhood of (xf,yf).