Wednesday, April 17, 2013

Prisoner's Dilemma: Our Love Story in a Nutshell (and a diagram)

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I am a huge fan of prisoner's dilemma. In fact, my wife married me because of it (not because it makes me a lot of money like it sounds like it should). To those who are unfamiliar, prisoner's dilemma is part of economic game theory that started with two economists at Princeton and which was further developed by John Nash (remember "A Beautiful Mind"?) and others. It shows why two individuals might not cooperate, even when doing so results in the best outcome for everyone. 


Katy cooperates (breaks up with boyfriend)
Katy defects (stays with boyfriend)
Clint cooperates (breaks up with girlfriend
Happy marriage (10,10)
Clint loses (0,5)
Clint defects (stays with girlfriend)
Katy loses (5,0)
Average Marriage (4,4)

Note: The numbers represent the payouts for each player. For example, if I choose to cooperate and break up with my girlfriend and Katy stays with her boyfriend (top right box), I get 0 "units of happiness" and Katy gets 5.

My wife Katy and I were both dating other people right before we got engaged. I realized when I ran into her at BYU after our LDS missions that she was the "one", and that we both needed to break up with our significant others to marry each other. However, the usual outcome of prisoner's dilemma is that both players end up with a sub-optimal outcome because of their fear of the other player defecting (i.e. if I broke up with my girlfriend and Katy stayed with her boyfriend, I lose everything, including my old girlfriend, and end up with nothing). As nerdy and as unromantic it sounds, I drew this diagram on a piece of paper and explained it to her in the library. We are now happily married with a "10" payout for both of us.

That's our love story in a nutshell and a diagram.

P.S. This theory is used in lots of other serious things like oil cartels in the Middle East, but I think my marriage example is the most practical application yet. Can I get a Nobel, anyone?

Note: Merrill Flood and Melvin Drescher were the ones who came up with the actual prisoner's dilemma. John Nash's famous equilibrium would have resulted in an "Average Marriage (5,5) in the lower right-hand corner.