On the power of unique 2-prover 1-round games

Abstract

A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games). The value of a 2-prover game is the maximum acceptance probability of the verifier over all the prover strategies. We make a conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conjecture.