Parallel repetition for all 3-player games over binary alphabet

We prove that for every 3-player (3-prover) game, with binary questions and answers and value < 1, the value of the n-fold parallel repetition of the game decays polynomially fast to 0. That is, for every such game, there exists a constant c > 0, such that the value of the n-fold parallel repetition of the game is at most n -c .

Along the way to proving this theorem, we prove two additional parallel repetition theorems for multiplayer (multiprover) games, that may be of independent interest: Playerwise Connected Games (with any number of players and any Alphabet size): We identify a large class of multiplayer games and prove that for every game with value