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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.

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    $\begingroup$ This is an interesting question, but it would be probably benefit from being clarified. I am guessing that what you mean is: Given a simultaneous game $G$ with strategy sets $S_1$,$S_2$ there is a set of equilibria $E$. If we consider the game variant $G'$ where player $1$ is allowed to send an observable signal (cheap talk or only zero sum?) the set of equilbria $E'$ is such that you can map each element $E'$ to an element of $E$ with the same elements of $S_1$ and $S_2$ being chosen. $\endgroup$
    – Giskard
    Sep 29, 2019 at 7:31
  • $\begingroup$ (Feel free to use any part of this should you choose to edit the question to clarify.) $\endgroup$
    – Giskard
    Sep 29, 2019 at 7:32
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    $\begingroup$ This calls to mind Crawford and Sobel's cheap talk model. If the sender and receiver's interests are diametrically opposed, then there is no equilibrium in which information is transmitted. $\endgroup$
    – user17900
    Oct 1, 2019 at 11:24

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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.

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