In "Fictitious play property for games with identical interests" by D. Monderer and L.S. Shapley, the convergence of fictitious play to a Nash equilibrium is proved for a potential game with players with identical interests. The case I am dealing in my research is a potential game where players have different utility functions, i.e. non-identical interests.
First, Is there any proof of convergence for this case? How about for other types of learning? In the case of existence, I do appreciate of any reference suggestion.
Second, Is there any convergence analysis for potential games with time-dependent potential function and time-dependent utility functions?