Friday, April 27, 2007

Game Theory and the Prisoner's Dilemma on the TV Show "Numb3rs"

The show mentioned this along with the scholar Anatol Rapoport who used the "tit for tat" strategy to win a prisoner's dilemma tournament. This game has applications in economics. I play it in my class then talk about how it relates to oligopoly in microecomics. Oligopoly is a market structure where a small number of firms dominate, like the auto industry. The idea in the prisoner's dilemma is that two criminals are being interrogated in separate rooms. It turns out that they would both be better off (in terms of how much jail time they will get) if they don't confess to a crime. But if one confesses while the other does not, the confessor gets alot less jail time while the one who did not gets alot more. So they each have a temptation to confess even though they would both be better off if they did not confess. How exactly this works is explained here and here. How things worked in the tournament that Rapoport won is described here. His method of playing turned out to be the best even though it was simple. How all of this works for the oligopoly and how those firms set prices is explained here.

In the tournament, players can choose two possible moves on each play: cooperate or defect. Cooperate means playing nice and not getting too greedy. Each player makes a move and gets points depending not only on what move they made but on what move the other player made. The "tit for tat" strategy means being nice (cooperating) but punishing (defecting) if the other player defects. If both players cooperate, they get more points than if they defect. But the temptation to defect is strong because if you defect when the other person is trying to cooperate, you get even more points (and the cooperator gets less). With the firms in oligopoly, cooperate is charge a high price. But the temptation is to defect, charge a lower price, and make more profit than your competitor. But then they start lowering the price, too, and you both make less profit than if you both charged a high price.

4 comments:

Carl said...

I agree with Robert Axelrod’s findings:
·Don't Be Envious
·Don't Be The First To Defect
·Reciprocate Both Cooperation and Defection
·Don't Be Too Clever

I found these attributes to be valuable while working with vendors who provided services for the companies I have worked for, as well as when working with so called competitors in order to share information that would make a produce Safer and Cheaper to operate. (In fact, this legal cooperation is actually encouraged by some Federal Regulating Agencies.)

It was always interesting to see the different approaches that my different employers had in developing contracts for services. Some companies had the approach that vendors were partners, thus they should get fair compensation for good quality services. In the end both companies would be better, and they both would survive to work with each other again and again.

The employer would who thought that getting the lowest price was the best way to go, always, ALWAYS, lost out in the long run!! Either the quality and turn times were below what was expected or required, and/or there was a constant battle to get even the simplest things accomplished.

No one wins if BOTH parties in a deal do not win!!!

That is why the Prisoners Dilemma game is so valuable for everyone, both student and seasoned employee to understand. When we played this game in class, out of 5 or 6 players I worked with, only one person understood cooperation!!! I never won a single game in our quick classroom demonstration, but this is not how it works in real life. Dr. Moron, may I suggest that your classes also read about the Robert Alexlrod’s findings in order to truly understand the lessons of this valuable classroom game.

Cyril Morong said...

Carl

Thanks again for visiting and commenting. I think you are right about how the "real" world works. Maybe when I play the game in class I should have more of an incentive, like a cash prize (just need a wealth donor). I do mention the tournament but I don't always mention Axelrod by name. Maybe I should have a handout that summarizes Axelrod's findings

Anonymous said...

I really love game theory and I can see it being a very important part of my life. If you have handouts on the subject, I would be pleased if you would oblige me.
For Carl,

I don't think your theory is correct about the employer and the best prices losing out. I will back my argument up by this one company that is a Huge Giant in the marketplace. W/o further ado, the place I am talking about is Wal-Mart. please correct me if I'm wrong.

Cyril Morong said...

To Anonymous

Thanks for dropping by. I don't have any handouts to post since the one I give out in class is just hand written. I think the links I provided give a decent over view.