Hyperbolic dynamics in Nash maps

R. A. Becker, S. K. Chakrabarti, W. Geller, B. Kitchens and M. Misiurewicz

Abstract

We investigate the dynamics of the Nash better response map for a family of games with two players and two strategies. This family contains the games of Coordination, Stag Hunt and Chicken. Each map is a piecewise rational map of the unit square to itself. We describe completely the dynamics for all maps from the family. All trajectories converge to fixed points or period 2 orbits. We create tools that should be applicable to other systems with similar behavior.