A Qualitative Characterization of Symmetric Open‐Loop Nash Equilibria in Discounted Infinite Horizon Differential Games

The local stability, steady state comparative statics, and local comparative dynamics of symmetric open‐loop Nash equilibria for the ubiquitous class of discounted infinite horizon differential games are investigated. It is shown that the functional forms and values of the parameters specified in a differential game are crucial in determining the local stability of a steady state and, in turn, the steady state comparative statics and local comparative dynamics. A simple sufficient condition for a steady state to be a local saddle point is provided. The power and reach of the results are demonstrated by applying them to two well‐known differential games.