JSM 2004 Online Program

Abstract #301624

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Activity Number:	379
Type:	Contributed
Date/Time:	Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor:	IMS
Abstract - #301624
Title:	Bootstrap Fictitious Play in Repeated Games
Author(s):	Dennis Gilliland*+
Companies:	Michigan State University
Address:	Dept. of Statistics and Probability, East Lansing, MI, 48824,
Keywords:	repeated play ; fictitious play ; online learning ; Hannan consistency
Abstract:	In repeated games, a player may use opponent's past moves in selecting a move for the present game. With fictitious play, the player plays Bayes against the empirical distribution Gn of those past moves. With bootstrap fictitious play, the player plays Bayes against the empirical distribution of an iid sample from those moves. Let regret denote the player's excess average loss over R(Gn), the component game Bayes envelope risk evaluated at Gn. For a class of component games, we show that the bootstrap fictitious play strategy has regret converging to zero uniformly in opponent's move sequences. The rate of this Hannan consistency is established.

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