Before revision:  Looking at the strategy composition, we retain equilibrium stationarity in general and  stability in potential games under admissible dynamics. Local stability of an equilibrium composition under any admissible dynamic can be tested by local stability of the corresponding aggregate equilibrium under the best response dynamic with i.i.d.~payoff perturbation. All the results are maintained under heterogeneity in revision protocols .
After revision:  Looking at the strategy composition, we retain equilibrium stationarity in general and stability in potential games are extended from the homogeneous setting to the heterogeneous setting. In particular, a wide class of admissible dynamics share the same set of locally stable equilibria in a potential game through local maximization of the potential .