Abstract and Applied Analysis
Volume 4 (1999), Issue 1, Pages 21-48

The turnpike property for dynamic discrete time zero-sum games

Alexander J. Zaslavski

Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Received 3 September 1998

Copyright © 1999 Alexander J. Zaslavski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).