Game theorists spend a lot of time thinking about signaling in situations where there is asymmetric information. These are cases where one player knows more than another player; the first player may want to signal something (for strategic advantage) or the second player may want to find out what the first player knows. This is exactly the stuff of linguistic pragmatics, so there are good reasons for linguists to think about information asymmetries and signaling. In particular, I want to think about cheap talk systems.
In a cheap talk system, it’s assumed that talk really is cheap: it costs little or nothing to send a signal. The effects of the signal depend on the strategic properties of the game under consideration. Consider a simple coordination game. Suppose we’ve decided to meet up. You don’t remember whether we decided to meet at a pub or a coffeehouse. You do know that we both prefer the pub to the coffeehouse and we prefer either of those to not meeting up at all. So here’s the game matrix:
Notice that both (pub,pub) and (coffeehouse,coffeehouse) are Nash equilibria; if we coordinate we have no reason to unilaterally defect. Both of us choosing the pub is Pareto efficient: it gives us the best possible payoffs.
I dropped my cell phone and broke it and you know that I don’t check my email very often but you can send a message to me in the hopes of meeting. You decide to send an email: “I’m going to the pub for our meeting.” Suppose I get the email. I should obviously go to the pub, since you have no reason to mislead me and every reason to tell me the truth. Therefore, (pub,pub) is the cheap talk equilibrium of the game. Notice that our interests coincide in this game.
Now suppose we’re playing a Prisoner’s Dilemma game:
In this game, if I squeal and you stay silent, I go free and you go to jail for a long term (the situation is reversed if you squeal and I stay silent). We both like going free so that gets the highest utility. We both hate long jail terms so that gets the utility zero. If we both stay silent, we both get a very short jail term based on another crime. We like that better than a long term but not as much as going free; I gave a short jail term a utility of 2. Finally, if we both squeal, we get medium jail terms, which is better than a long term but not as good as a short jail term; it gets a utility of 1.
Notice that the action of staying silent is dominated by squeal. If you’re silent, I can defect and squeal. This gets me out of jail free. If you squeal, then I had better squeal too; otherwise, I go to jail for a very long time, my least favorite outcome.
There’s an intuition, though, that we both ought to stay silent. This gets us both a payoff of 2, which is better than the payoff of 1 we get if we squeal. But because of the temptation payoff, (silent,silent) is not a Nash equilibrium. We’re both drawn to the temptation payoff we get if we squeal and the other player is silent. So we wind up with the mediocre payoff we get under (squeal, squeal).
Now, suppose I can send you the message “I’m going to stay silent.” Should you believe me? Well, talk is cheap so you’re well advised to assume that I’m trying to trick you. If you believe me and stay silent, then I have every incentive to squeal; you’d better squeal too, if you want to avoid a long jail term. If you think I’m sincere, then you ought to squeal, since you’ll get your preferred outcome. In any event you should just squeal. So my message has no real effect on your behavior; there’s no cheap talk equilibrium. Rather there’s a “babbling equilibrium.” I might just have well said “ooga booga” for all the good it did!
Now you might think that I should keep my word; but this assumes that there are consequences for my duplicity: That’s a different game. In this instance, we can assume that if I squeal and go free, I can just fade into the woodwork (or the witness protection program) and go on with my life, no consequences for my betrayal.
Linguists find the cheap talk framework a bit peculiar; of course we should take the costs of speech production into account! Suppose, for example, that I have to choose between using a pronoun like “it” and a full description like “the pen on the table over there.” Of course, producing the pronoun is relatively inexpensive so if I think you’ll interpret it correctly, I’m likely to use it. It costs less effort for me to produce it than the relatively long description. If, however, I think you won’t interpret the pronoun correctly, then I’ll go to the effort of producing the long description; this has higher production costs—I have to decide what description to use and then actually produce it, which is work—but it’s at least likely to have the desired effect.
The fact that we use pronouns at all shows that considerations of production costs do impact our linguistic behavior. So talk isn’t always cheap.
Notice that there’s an effect of scale here. At the micro-level of speech production, considerations of production costs have an impact on our behavior. At the macro-level of influencing your strategic decision-making, then talk is cheap: I’ll certainly go ahead and produce the signal if I think it’s to my strategic advantage to do so.
Sometimes, of course, talk isn’t cheap even at the macro-level. Suppose that I develop a reputation as deceitful in a population. Other members of the population assume that I’m a liar and are less likely to cooperate with me. They might even refuse to play. In that case, talk has damaged my social standing, my “face” in the terms of Erving Goffman, and I become less capable of getting things done socially. Then talk certainly isn’t cheap.
I’ll almost certainly be returning to face in other posts; I think it’s an important principle organizing a lot of our linguistic behavior.