Stability of mixed equilibria in interactions between two populations

This paper considers Nash equilibria of a game played by two populations. Stability of the mixed equilibria is diacU8aed for a wide class of differential systems describing the evolutionary dynamics of behavior. The main property of the Systems under consideration is that every Nash equilibrium of the game is a fixed point. The paper shows that no mixed equilibrium is linearly asymptotically stable for the autonomous systems of this class. It also establishes that linear instability of the said Nash equilibrium for an autonomous system leads to its Liapunov instability for any corresponding non-autonomous System.