August 25, 2014
Something on the lighter side from Epsilon Theory today, as summer winds downs here in the last week of August. Most of us have seen videos galore of the ALS “ice bucket challenge,” and I thought it might be interesting to recast a classic game theory construct – The Prisoner’s Dilemma – in ice bucket terms. So I enlisted my four daughters to be prisoners and wardens with the following scenario.
If both prisoners choose a green card, I’ll donate $100 in each prisoner’s name to ALS research. If one prisoner chooses green but the other prisoner chooses red, I’ll donate $250 in the name of the red-choosing prisoner but $0 for the green-choosing prisoner, and a warden will dump an ice bucket on the head of the green-choosing prisoner. If both prisoners choose a red card, I’ll donate $50 in each prisoner’s name, and both wardens will dump an ice bucket on her prisoner.
Both prisoners know the payoffs, but they can’t see each other and can’t communicate with each other. In 2×2 matrix form (see “Through the Looking Glass” for another example), the game looks like this:
As with all PD games, joint cooperation (2 green cards) is a much better outcome for both players than joint defection (2 red cards), but the stable equilibrium as marked by the blue oval is joint defection, with half as much money donated to ALS research and a bucket of ice water on your head to boot.
The results? Well, see for yourself in the video below!