Parallel Repetition in Projection Games and a Concentration Bound

In a two player game, a referee asks two cooperating players (who are not allowed to communicate) questions sampled from some distribution and decides whether they win or not based on some predicate of the questions and their answers. The parallel repetition of the game is the game in which the referee samples n independent pairs of questions and sends 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 [Raz98, Hol07], which showed that the players cannot win all copies in the repeated game with probability better than (1-3 )(n/c) (here c is the length of the answers in the game), in the following ways:

• Type: Journal
• Year: 2008
• Where: ECCC
• Authors: Anup Rao
• Keywords: ECCC 2008, Game, Parallel Repetition, Questions