Wednesday, February 23, 2005

Game theory...what have we got to do with it?

Mathematics, if done for hours, can be frustrating. Think about engineers, in every professional major course, we have mathematics at an application level. That isn’t all that interesting. Thankfully we have Humanities course, which is like a stress reliever. Environmental and resource economics is an interesting course. The title seems like a contradiction of sorts. How can an economist think of conserving environment??? Well, environmental economists claim they do.

The course began with a generic overview of economy. We were given a small glance at the problem of “the prisoner’s dilemma” in game theory and its relevance in making economic decision. If you already know the problem, couple of paragraphs can be skipped.

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Here’s the problem, two prisoners are given the choice of denying or confessing to a crime. The consequences of their decision are as tabulated

If A and B confess, both get 3 years.
If A confesses and B denies, A gets 0 years and B get 5. (Vice versa)
If both deny, each get 1 year

The catch is, they are not allowed communicate.


Look at this from A’s perspective, he is better of confessing than denying, simply because maximum sentence in confession is just 3 years while for denying costs him 5 years. One can safely assume that B would think on similar lines and confess. Both of them end up spending 3 years in jail. 6 man years are lost. The sub-optimal strategy was the result of lack of communication. If both had denied, only 2 man years would have been lost!

Some economic decisions are taken in isolation, which could often result in sub-optimal strategy.

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I hadn’t paid attention to this until the saarang JAM competition thinking it’s just a theory. The moderator conducted a round in which, the buzzers between two participants were exchanged. Consider speakers 1 and 2. If speaker 1 buzzes, speaker 2 has to point out the error. If speaker 2 fails, 1 has to point out the error. Here speaker 2 wins 10 points and speaker 1 wins 5 points if speaker 2’s objection is sustained. When speaker 2 fails and speaker 1 points out the error, speaker 2 loses 5, and speaker 1 gets 10. If both of them fail, speaker 2 loses 5, and speaker 1 looses 15.

It is interesting that in order to pull down speaker 2 by unnecessarily buzzing, speaker 1 also has to lose. We end up in lose-lose situation. If every one follows the rules and buzzes legitimately we have a win-win situation. This is much like the prisoners dilemma, looking for a ‘win-win’ situation rather than a ‘lose-lose’ or a ‘lose-win’ one. One might think this was an obvious situation, it’s a game, and rules have to be fair without loop holes. My point is that the idea of ‘win-win’ strategy being more optimal is reflected well here.

About a year ago, the administration of IIT was deciding on shuffling the 1st year students of different hostels. Most of the students, including seniors, did not want this. At some point, I thought about boycotting the institute student body elections if our ‘fate’ wasn’t known by then, though I didn’t express it.

I should call myself irrational here. Boycotting elections would, in some probability, result in ‘fractured mandate’. Had that happened, student community in general would have been a loser. Further more, if we were indeed shuffled, we would have been losers again. I was looking at a ‘lose-lose’ (or a ‘lose-win’, shuffling wasn’t certain) option then. Fortunately, no one got shuffled (except sarayuites) and we all did vote. That was ‘win-win’, wasn’t it?

An abstract mathematical concept integrates itself to daily life without us realizing it. It’s surprising, isn’t it?


# posted by Shankar : 4:31 AM
Comments:
Nice post man and pseud blog.

Prisoner's Dilemma can be applied with great effect at many places. Some examples: the deadlock in the parliament, the constant tug between monetary policy (under the control of RBI) and fiscal policy (under the control of government) and closer to home, our approach to apps.

Pseud post again, it is hard to see such nice thinking on blogs.

-Middle. (The Pub man)
# posted by Anonymous Anonymous : Tue Dec 20, 12:16:00 AM 2005
 
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