There's no particular way I see to coordinate on a "yea" answer. You don't have any ability to coordinate with others while you're answering questions, and "nay" appears to be the better bet before the problem starts.

It's not uncommon to assume that everyone in a problem like this thinks in the same way you do, but I think making that assumption in this case would reduce it to an entirely different and less interesting problem -- mainly because it renders the zero in the payoff matrix irrelevant if you choose a deterministic solution.