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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?

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    $\begingroup$ See Ch. 6 of "Strategic Learning and its Limits" by H. Peyton Young. $\endgroup$ – Ronaldo Carpio Mar 12 '15 at 5:54
  • $\begingroup$ @RonaldoCarpio, Many thanks for your help. I have searched for the book (even on sites such as gen.lib.rus.ec) and couldn't find it. Also the university doesn't have it. Do you know any other reference or the pdf of the book? Many Thanks! $\endgroup$ – Mohammad Khosravi Mar 12 '15 at 8:19
  • $\begingroup$ You can try Zafra, "Fictitious Play Algorithm" in the Wiley Encyclopedia of Operations Research and Management Science. Also, see Berger (2007), "Brown's original fictitious play". $\endgroup$ – Ronaldo Carpio Mar 12 '15 at 12:23

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