Signaling in zero-sum games? The foundation of this question is a bit vague (based on something overheard at a conference) but I'm hoping someone here can provide some clarification. 

I overheard a conversation between two people at a conference saying that signaling doesn't really make sense in zero-sum games. Unfortunately, I don't have much more context than that.

I have continued to think about this statement and really can't figure out why it ``doesn't really make sense.'' The zero-sum aspect only talks about the payoffs, where the signaling aspect is concerned with how information is revealed as a function of the players' actions. I don't see why a game being zero-sum should preclude signaling.

Question: Can signaling occur in zero-sum games? Please provide a link to a paper/example if so.
I just taught my students that signalling is useless in Matching Pennies and Rock, Paper, Scissors. You would just lie and be random anyway so why would the other player ever believe any signal at all? That renders signals useless. Perhaps the people you overheard meant just that.