  We use a recently discovered constrained de Finetti reduction (aka
"Post-Selection Lemma") to study the parallel repetition of multi-player
non-local games under no-signalling strategies. Since the technique allows us
to reduce general strategies to independent plays, we obtain parallel
repetition (corresponding to winning all rounds) in the same way as exponential
concentration of the probability to win a fraction larger than the value of the
game.
  Our proof technique leads us naturally to a relaxation of no-signalling (NS)
strategies, which we dub sub-no-signalling (SNOS). While for two players the
two concepts coincide, they differ for three or more players. Our results are
most complete and satisfying for arbitrary number of sub-no-signalling players,
where we get universal parallel repetition and concentration for any game,
while the no-signalling case is obtained as a corollary, but only for games
with "full support".
