A general model of best response adaptation

We develop a general model of best response adaptation in large populations for symmetric and asymmetric conflicts with role-switching. For special cases including the classical best response dynamics and the symmetrized best response dynamics we show that the set of Nash equilibria is attracting for zero-sum games. For asymmetric conflicts and equally large populations, convergence to a Nash equilibrium in the base game implies convergence to a Nash equilibrium on the Wright manifold in the role game.