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learning-s - Joint Strategy Fictitious Play Sherwin Doroudi...

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Joint Strategy Fictitious Play Sherwin Doroudi
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“Adapted” from J. R. Marden, G. Arslan, J. S. Shamma, “Joint  strategy fictitious play with inertia for  potential games,” in  Proceedings of the 44th  IEEE Conference on Decision and Control December 2005, pp. 6692-6697.
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Review: Game • Players: • Actions: • Payoffs:
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Review: Game We then play the game repeatedly in  “stages,” starting at stage 0.  Players  can use learning algorithms as  discussed in lecture.  Note that  players know the structural form of  their own payoff function, but do not  know the form of the other players’  payoff functions.
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Notation: Actions As in the lecture, we use the notation
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Review: Regret Matching Guaranteed to converge to a Coarse  Correlated Equilibrium (CCE) in all  But CCE can be quite bad in some  cases, as they are a superset of Nash  Equilibria (NE).
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Review: Fictitious Play (FP) Observe empirical frequencies of  every player’s action Consider best response(s) under the  (incorrect) assumption that other  players play according to their  empirical frequencies Randomly choose a best response and  act accordingly
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Empirical Frequency in FP The empirical frequency for a player  and an action is the percentage of  stages that the player chose that  action up to the previous stage:
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Empirical Frequency in FP Each player also has an empirical  frequency vector.
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Best Response in FP Each player assumes an expected payoff And each player chooses a best response  from the set
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This document was uploaded on 01/05/2012.

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learning-s - Joint Strategy Fictitious Play Sherwin Doroudi...

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