A Generalized Model of Best Response Adaptation

We present a generalized model of myopic best response adaptation in large populations. In asymmetric conflicts, individuals can be in the role of the row player or the column player. The idea that an individual's role need not be fixed is introduced explicitly in our model by a process of role switching. The best response dynamics, the symmetrized best response dynamics, and the continuous time fictitious play process are included as special cases. We show that the set of Nash equilibria is attracting for zero-sum games. Moreover, for any base game, convergence to a Nash equilibrium implies convergence to a Nash equilibrium on the Wright manifold in the role game.