This post is about an incident from the Wendy Williams talk show. A wife says her husband promised they would have two children. But after the first child, the husband did not want another.

The woman really wants another child. She is considering secretly stopping her birth control medicine to trick her husband into having another child. What should she do? Here is the clip from the show.

Wendy Williams explains couples should normally discuss their problems. But in this case she says women have control over their bodies and it is fine. Does everyone agree? The audience, nearly all women, applauded.

The advice was controversial and in this post we discuss it from a game theory perspective.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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A Game of Trust

Let’s abstract the situation into a strategic setting. The wife has two broad choices of discussing (D) the situation with her husband or tricking (T) him by going off of birth control. Presumably she has fear about discussing the situation because of her perception of what the husband might do. He might be mature and choose to discuss (D) the situation–in which case they come to a reasonable compromise. But he can also act unilaterally and secretly trick (T) the wife into his choice of one child, by say, having a vasectomy.

The payouts to this game resemble a prisoner’s dilemma:

–if they both discuss, it builds trust

–if only one tricks, that person gets what he/she wants and “wins”

–if they both trick the other, they destroy trust

The overall best outcome is that the married couple discuss the problem and try to understand the problem from the other side’s view. But each has an incentive to trick regardless of what the other person does.

What does game theory predict?

In a single-shot interaction, both sides will trick the other and they will not be able to trust each other in the future. In a repeated game with an unknown horizon, there is a possibility for building trust: each party recognizes that tricking the other is destructive, and the short-gain from cheating is not worth the long-term loss of trust.

There is a code in marriage to discuss and be open, and that is precisely to encourage behavior to build trust. Wendy Williams was blasted for encouraging an action that would ruin the trust.

But even then there is a lesson in her advice. She said that normally she encourages couples to trust each other. That is, even she recognizes that long-term trust is worth more than tricking the other person for something small.

That breaks down, however, when the gain from a one-time score outweighs the long-term trust. And this is the real game theory lesson: when someone cheats you in a game of trust, it will be for something big.

The irony is the plan may have worked. Since birth control is not 100 percent effective the husband may never have known. But there is a silver lining to the story. It is hard to take the plan seriously, because it’s really hard to trick someone when you announce the plan on national television.