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Summary: Parallel Repetition in Projection Games and a Concentration
Bound
Anup Rao #
University of Washington
anuprao@cs.washington.edu
September 17, 2010
Abstract
A two player game is played by cooperating players who are not allowed to communicate. A
referee asks the players questions sampled from some known distribution and decides whether
they win or not based on a known predicate of the questions and the players' answers. The
parallel repetition of the game is the game in which the referee samples n independent pairs of
questions and sends the corresponding questions to the players simultaneously. If the players
cannot win the original game with probability better than (1 - #), what's the best they can do
in the repeated game?
We improve earlier results of [Raz98] and [Hol07], who showed that the players cannot win
all copies in the repeated game with probability better than
(1-#/2)# n# 2 /c) (here c is the length
of the answers in the game), in the following ways:
. We show that the probability of winning all copies is (1 - #/2)
# #n) as long as the game is
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