David Cameron, credit cards and game theory

The first version of David Cameron’s speech to the Conservative party conference contained a call to households to pay off their credit card debts.

What’s the game theory of paying off your personal debts?

We might represent the situation through the table below (if you haven’t seen this sort of thing before then check out this post). It shows a simplified version where we think about two people who have the choice to pay off their credit card or not.

If both people pay off their cards then the lack of consumer spending means that the economy falls back into recession, we consider this the worst outcome.

If both players don’t pay off their debt then there is still spending to support the economy but each person still has to carry a pile of debt. Not great but better than the recession scenario.

If one player pays off their debt and the other one doesn’t, then the one who pays off their debt is better off, the one who doesn’t is worse off. But not as badly off as if both players pay off their debts.

This game now looks like a game of chicken. Normally a game of chicken is represented by two drivers driving at each other. The worst result is if neither swerves as they then crash. Both swerving is better but each player really wants the other one to swerve out of the way while they carry straight on.

In the credit card debt game each player would rather pay off their own debt, but only if the other player doesn’t.

Any call by the Prime Minister for everyone to pay off their debts could have led to an almighty car crash. The debts need to be slowly cleared so that not too many cars crash into each other all at once.

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