A parallel repetition theorem

We show that a parallel repetition of two-prover oneround proof systems (MIP(2, 1)) reduces the probability of error at an exponential rate. This settles a standing open problem, sometimes called 'The Parallel Repetition Conjecture". Previously, no constructive bound was known. The constant we have in the exponent is logarithmic in the total number of possible answers of the two provers. This is significantly better than what was previously known even in the much stmpler case