One Utah

Recently, I’ve been doing some reading into game theory.  Classic game theory works on the premise that each person is a rational actor (as in classic economic theory) and will act to maximize the benefit to themselves.  Contemporary game theory however holds that how people perceive self-interest is different than traditional game theory holds; people will at times make choices that don’t benefit them in traditionally rational ways but which work to their perceived benefit.  Game theory teaches us that collaboration is actually more beneficial than cooperation, the trick is apparently to figure out with whom to cooperate.

Case in point:

In one experiment called “traveler’s dilemma,” two students chose numbers from a range. Each would get cash equal to the lower of the two numbers picked–for instance, $150. That means they would do best if both picked high numbers. But there was a counterincentive: The student who chose the higher number had to pay a $5 penalty. The game was played just once so the students couldn’t learn cooperation. By Nash’s theory, each should have tried to undercut the other just a bit to avoid the $5 penalty. In doing so, both inevitably would have chosen the lowest allowable number. In real life, though, most of the students picked the highest allowable number, to their mutual benefit. As long as the penalty for being the high-number picker was small, there was no “race to the bottom.”

So what happens here is a different kind of calculating - in this case we both come out better so who cares if one of us pays a small penalty.  The only scenario in which this doesn’t work this way is if we hate each other and want to hurt each other.  If the penalty is larger - say $50 not $5, that changes how we figure the benefit of the game.  It’s a question of whether or not the penalty is a disincentive.

Another classic game theory example is the Prisoner’s Dilemna.  Summary:

You and a colleague have committed a crime.  You are being interviewed in separate rooms.  If neither of you confesses, the police can prove you committed a lesser crime and you each get one year in jail.  If you confess and turn state’s evidence and your colleague does not confess, you go free and your colleague gets twenty years in jail (and vice versa if they confess).  If you both confess you each get ten years in jail. 

The traditional solutions assumes your colleague will try to maximize their personal benefit and confess, so you should confess.  In the end both of you confess and receive ten years in jail.  The risk is that your partner will confess and you won’t - which means you get twenty years.  The game is structured in such a way that it is to both of your benefits to confess. 

But look at the example again - if you know that the police are going to try this trick on you, then you cooperate with each other against the police and get one year apiece.  The argument is made that your motive is to confess because you go free, and even if you both confess, the outcome is better for each of you (ten years not twenty in jail).  But it seems to me that time in jail is a certain outcome of the game - so your goal should not be to go free at this time but to minimize your time in jail.  You should both refuse to confess - not to go free but to get the least amount of time in jail. 

Here’s where I depart from both traditional economics and game theory - trying to go free is the “rational” goal but in this case, I disagree with the traditional assumptoins about what is rational.  In the scenario going free is not a possible outcome for either colleague.  If you accept the idea that time in jail is inevitable, then my choice seems eminently rational.  Maybe it’s changing the rules of the game, but all the advantage in the Prisoner’s Dilemna belongs to the police - the prisoners have are completely trapped.  So change your assumptions going in and you change your behavior. 

If you watch any Law and Order, you know the prisoner’s dilemna never works out for the prisoner - the minute somone confesses, they get arrested.  Even if they go free on one crime, they get jail on another.  So if you change your expectation of the “rational” outcome from going free to minimizing your time in jail, it makes a difference in how you choose to behave.  In essence, if you are the criminals, you agree in advance that you know if you get caught you’re going to get jail time - assume the police are dishonest and will lie about you going free.

Game theory teaches us that collaboration and cooperation usually benefit us more than competition.  The question, as I said, is to carefully consider with whom and how to cooperate. 

This entry was posted Friday, March 21st, 2008 at 10:31 am and is filed under This Blog, Uncategorized. You can leave a response, or trackback from your own site.