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Respond to the question: learning in ficticious play?

01/14/2001 08:52 PM by David K. Levine; frequencies versus assessments
The convergence of frequencies and assessments is the same, since the relative weight of prior to the weight of the sample goes to zero. Using priors makes the procedure better behaved in small samples (and in particular makes it
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01/03/2001 03:31 PM by Christine; learning in ficticious play
Hi! Sorry for my blank entry... A question from Paris about learning in games, and fictitious play. I have read two books : Fun and Games from Ken Binmore and The Theory of Learning from Drew Fudenberg and David Levine.

I found in Binmore that assessment of each player about the distribution of opponent's action is given by the frequency of opponent's play, that is if, after n stages, player 1 has played k times his second action, player 2 believes that player 1 chooses his second action with probability k/n. All the Binmore's analysis lies on frequencies each player play his actions. The fictitious play can be defined by a rule that assigns a best response to each frequency. But nothing is said about the start of the play. Nevertheless, Binmore draws the convergence of a fictitious play towards a mixed Nash equilibrium with an interior starting point. How this can be possible?

In Fudenberg and Levine, I read that each player has an exogenous initial weight function. And stage after stage, the weights are updated by the play of each player and give their assesments about the opponent's behavior. So, in Levine and Fudenberg, we have two things : the assesment which is function of the weights and the marginal empirical distribution of plays. They define the fictitious play by a rule that assigns a best response to each assessment and not to frequency. But they still analyse the convergence of frequencies. Then, what is important? The convergence of frequencies or the convergence of assessments? Why don't they simply use the frequencies like Binmore for the analysis of fictitious play? [Manage messages]