The Prisoner's Dilemma

I'm continuing my tour of Poundstone with "The Prisoner's Dilemma" This is a history, Game Theory, the people that created it, it's use and impact on history, and a few simple games…

 

Stag Hunt. This is a game similar to the tragedy of the common. To hunt a stag, you need two or more people working independently. While you are hunting, there is no guarantee that you will land a stag. It would be best if you did, but it's long hard work. Now, if you take a detour while searching for a stag, and hunt some easy to find birds instead, then it's ok for you, since you've found a little food, but your hunting partner won't succeed.

 

Deadlock—a situation where it's best for opponents to keep fighting.

 

Chicken—Two people drive headlong towards each other. The one who swerves is the chicken. If neither swerve, then both die.

 

Prisoners Dilemma. Two prisoners are being questioned about a crime in separate rooms. Each is offered a choice… "If you rat out the person in the other room, then you will get a lesser sentence. The other person will get a long sentence." But, if both of you stay silent, then you both go free. Would you trust the person in the other room to not rat you out?

 

Suckers Bet—A dollar bill is put up for auction. You can bit any amount and bids continue until there are no more. The catch is that the 2^nd last person who bids also has to pay his bid, but gets nothing in return. What's vicious about this game is that if someone pays $1.00 to buy the $1.00, then it makes sense for the person who bid 95 cents to bid $1.05 to get the dollar, since he will loose five cents by over paying, but 95 cents if he comes in second place.

 

Iteration—the dynamic of many games changes if you play the prisoners dilemma, or chicken once, then the strategy is very different than if you have to play it repeatedly—the best way to get cooperation is through an ongoing relationship and not a one shot transaction.

 

With many of these games, chicken is the best example, it's the most unstable party who has the advantage. This is not a happy thought.

 

Tit-For-Tat. This is a very robust strategy for dealing with iterative games. Many strategies only work if they are secret, if other people figure them out, then they loose there value. But, Tit-For-Tat works well when everyone knows that's how you operate. It works well if everyone plays that way.

 

The one catch with Tit-for-Tat is that the size of the Tit must be the same as the size of the Tat. If the two are different (perhaps due to subjective judgement) then Tit-for-Tat can spiral out of control with endless tit's responding to subjective tat's.