In a role game, players can condition their strategies on their player position in the base game. If the base game is strategically equivalent to a zero-sum game, the set of Nash equilibria of the role game is globally asymptotically stable under the best response dynamics. If the base game is 2...

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...