The Sound of Silence


Silence can be a powerful signal. For example, imagine that you have a friend who is a female college student. You see your friend kiss a boy who looks like he is in high school. You estimate he is 13, 14, 15, or 16. It would be very embarrassing for a college girl to be caught kissing a boy that young.[7] Assume that your friend’s honesty would prevent her from ever lying to you. If she told you the boy was 16, you would believe her. While she won’t lie, she would be willing to tell you to “mind your own business.” When you ask your friend how old the boy is, what should she say?

Obviously, the older he is, the less embarrassed she will be. She knows that there is no way you would ever think he is over 16. Thus, if he is 16, she will tell you. If he is 16, she wouldn’t, by assumption, lie. If she says, “Mind your own business,” you might think he is 16, but you also might think that he is younger. Consequently, if he is 16, she will always make herself look better by revealing it.

Now let’s assume that the boy is only 15. What should she do? Her choice is either to say 15 or to tell you to “mind your own business.” If she says, “Mind your own business,” however, you will know the boy could not possibly be 16 because, recall, if he is 16, she would reveal it. Thus, if she employs her “none of your business” strategy, you will believe that the boy is 15, 14, or 13. Since she would rather you think him 15 than 13 or 14, she will reveal his age if he is indeed 15.

Now pretend that the boy is really 14. If she says, “Mind your own business,” you will assume he can’t be 15 or 16 and thus must be either 13 or 14. Since it will be better if he was 14 than 13, she should reveal his age if he is indeed 14.

We have established that your friend will tell you the boy’s age whenever he is 14, 15, and 16. Consequently, if she says, “None of your business,” you know the boy is 13. This is a stable outcome, for if you assume that “none of your business” means 13, it will be in your friend’s interest to tell you his age, unless he is indeed 13. Since your friend can’t lie, she must reveal the truth. Game theory thus establishes that she can’t really stay silent, since silence tells you the boy is only 13.

The key result from this game is that when a player can’t lie, she also can’t stay silent, for silence communicates information. Silence signals that the situation is very bad because if it wasn’t, you would have an incentive to say something. This result has strong applications to consumer product markets.

Imagine that widgets are a tasty food that comes in two varieties: (1) safe widgets, which cause no ill health effects, and (2) unsanitary widgets, which induce vomiting. You’re in the grocery store and see some widgets labeled as safe and some with no label. Assume that consumer fraud laws prevent makers of unsanitary widgets from labeling them as safe. What should you assume about the unlabeled widgets? Obviously, if they were safe, their producer would benefit from labeling them as such. Thus, the lack of a label signals that the widgets are unsanitary. In a deep sense, therefore, all the widgets are labeled.

Now imagine that instead of being safe or unsanitary, widgets are either high or low in fat. Since most consumers prefer low-fat foods, manufacturers of low-fat foods will label their products as such. Thus, no label means high in fat.

When a product is not labeled for some characteristic, you should assume that either most people don’t care about the trait, or that the product’s trait is bad. Even if the trait were average, it would be labeled. Since good traits are always labeled, if a product is not labeled, customers will assume that its quality is well below average. Consequently, firms will find it in their self-interest to label products of merely average quality.

In U.S. criminal trials, defendants are not required to testify. A rational jury should conclude that if the defendant doesn’t testify, he must realize that testifying would hurt him. Thus, a rational juror would learn a lot from a defendant’s refusal to testify. In U.S. courts, however, juries are prohibited from drawing any inference from a criminal defendant’s refusal to testify. Juries are thus supposed to be irrational and forget what a defendant’s non-testifying signals.[8] (If you want to get out of jury duty, then when asked if you could fairly judge the defendant, you should warn the court that if the defendant doesn’t testify, you will assume that he has something to hide.)

While juries are sometimes supposed to be irrational, businesspeople should always listen to the sound of silence. If information is not disclosed, you should often assume the worst. For example, if a job candidate has several holes in his r sum , you should assume that he was afraid to fill in the gaps.

[7]Many Smith College students have told me that it would indeed be embarrassing to be seen kissing a 13-, 14-, 15-, or 16-year-old boy.

[8]See Baird, Gertner, and Picker (1994), 79–121.




Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
ISBN: N/A
EAN: N/A
Year: 2005
Pages: 260

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