Robust product self-testing conjecture for synchronous games

Let $\mcG_1$ and $\mcG_2$ be two synchronous games. Robust product self-testing conjecture. The product game $\mcG_1\times\mcG_2$ is a robust self-test for its perfect strategies if and only if both $\mcG_1$ and $\mcG_2$ are robust self-tests for their perfect strategies. The preceding exact product and parallel-repetition results for ordinary self-testing motivate this robust analogue; its status is not established in the supplied text.