We give a three-player game whose non-signaling value is constant (2/3) under any number of parallel repetitions. This is the first known setting where parallel repetition completely fails to reduce the maximum winning probability of computationally unbounded players. We also show that the best known results on non-signaling parallel repetition apply to a relatively limited class of games. In particular, these games cannot yield log-prover MIPs for languages beyond PSPACE.
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