Thursday, May 10, 2007

Managers' Dilemma?

One of the best explanations of Prisoner's Dilemma: (In the words of Douglas R Hofstadter, from Metamagical Themas)---
Life is filled with paradoxes and dilemmas. Sometimes it even feels as if the essence of living is the sensing---indeed, the savoring---of paradox. Although all paradoxes seem somehow related, some paradoxes seem somehow related, some paradoxes seem abstract and philosophical, while other touch on life very directly. A very lifelike paradox is the so-called "Prisoner's Dilemma", discovered in 1950 by Melvin Dresher and Merril Flood of the RAND Corporation.

Assume you possess copious quantities of some item (money, for example), and wish to obtain some amount of another item (perhaps stamps, groceries, diamonds). You arrange a mutually agreeable trade with the only dealer of that item known to you. You are both satisfied with the amounts you will be giving and getting. For some reason, though, your trade must take place in secret. Each one of you agrees to leave a bag at a designated place in the forest, and to pick up the other's bag at the other's designated place. Suppose it is clear to both of you that the two of you will never meet or have further dealings with each other again.

Clearly, there is something for each of you to fear: namely, that the other one will leave an empty bag. Obviously, if you both leave full bags, you will both be satisfied; but equally obviously, getting something for nothing is even more satisfying. So you are tempted to leave an empty bag. In fact, you can even reason it through quite rigourous this way: "If the dealer brings a full bag, I'll be better off having left an empty bag, because I'll have gotten all that I wanted and given away nothing. If the dealer brings an empty bag, I'll be better off having left any empty bag, because I'll not have been cheated. I'll have gained nothing but lost nothing either. Thus it seems that no matter what the dealer chooses to do, I am better off leaving an empty bag. So I'll leave an empty bag.

The dealer meanwhile, bring in more or less the same boat (though at the other end of it), thinks analogous thoughts and comes to the parallel conclusion that it is best to leave an empty bag. And so both of you, with your impeccable (or impeccable-seeming) logic, leave empty bags, and go away empty handed. How sad, for if you had both just cooperated, you could have each gained something you wanted to have.

Does logic prevent cooperation? This is the issue of the Prisoner's Dilemma.
Prisoner's Dilemma is one crucial concept towards the Game Theory.

Now, on to the Beautiful Game:

Last night's drub goalless draw between Manchester United (the new champions) and Chelsea (the defending champions) was probably inspired from this (logical?) non-cooperation principle. Both the managers rested their major players, perhaps in preparation of the FA Cup final at the new Wembley Stadium. In all these game theoretic tactics, to say the least, the fans were at a great loss, as the match ended with a lot of bookings and no goals on the scoresheet!

Perhaps you can sense how boring the game would have been just from the post match report!

1 comment:

Anand Sarolkar said...

Liked the concept of Prisoner's dilemma!