Mauricio Medinaceli Monrroy
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Cooperative Games: How not to die trying?

"Should I cross in red?" Your head starts wander with questions unanswered: What would happen in a society without rules? Why should I respect the red when it's inefficient for me? Where is the police? Why I am the type of person who respects red at twelve o'clock at night?

If ever, dear reader, you faced this kind of moral dilemmas, let me tell you that you're not only one, in fact, is a classical dilemma in the social sciences, particularly economics. For this reason, I want to share with you some ideas about cooperative relationships and stable equilibrium.

In an excellent book title "Prisoner's Dilemma" by William Poundstone, the author tell us the exciting life of John von Neumann, outstanding Hungarian scientist who worked at RAND institute and made notable contributions to what is now called Game Theory. With genius extravagant tastes and passionate about exact sciences, von Neumann developed important contributions to social sciences, mathematics, statistics and other... in fact, according to the author of this book, Professor von Neumann laid the foundation for personal computers and cell phones, 60 years ago!

But... Why is it important "Prisoner's Dilemma"? First, was Professor Albert William Tucker (well known by economics students because the "condition of Kuhn-Tucker") who put the name to the cooperation model developed by Flood and Dresher. Second, in economy we call "games" to the interrelationships between two or more agents (individuals or companies) under a given set of rules, from chess to pricing strategies by oil exporting countries (OPEC). Third, its importance lies in the possible outcomes of this relationship, certainly the winner of chess game will have our admiration, but the price resulting from a oligopolistic behavior of OPEC countries will affect our pocket. Fourth, because this model of cooperation touches us every day... as I'll describe below.

The model is very simple, two prisoners are captured and interrogated in separate rooms. If both don't reveal (behave like real friends) there is no sufficient evidence and are sentenced to, say, one year in prison. If both (very unfriendly) will reveal then they are doomed to, say, five years in prison. If one betrays and the other not, we will have a good friend and a traitor, traitor will not go to jail and the other friend will be 10 years in prison. Solved the game, it appears that the most often results it's that both prisoners betray each other and then each will spend 5 years in jail. One might think why they couldn't agree don't betray each other and only spent 1 year in jail? It turns out that the incentive to be free, makes both betray each other and therefore achieve a non-cooperative solution... like a couple of fools.

Is this crazy? No. Sometimes human beings act non-cooperatively, here some examples: 1) if all we will have respect for red traffic light would be great, but it's enough that someone doesn't to create chaos; 2) when we bought tickets for a concert, we all do the "row" but if someone doesn't he/she will create a worst equilibrium; 3) two companies decide to charge a minimum price, but is enough if one company decrease a little bit the price to reach insane price levels; 4) all agreed to pay taxes, but if somebody doesn't pay and still get public goods and services benefits, then the rest of the people will not pay taxes anymore; as you may see, we live in a world where cooperation is a fundamental part of our actions, so economists spent a lot of time studying cooperative solutions, because a cooperative world seems better. Education, age and even gender (women are always good) explain very well the desire to cooperate.

And so, dear reader, when you are reading a book or a newspaper, waiting for a taxi or bus, or going home... raise your eyes, look around and think about cooperative societies, for sure, you'll remember professor John von Neumann and Professor Tucker.

Mauricio Medinaceli Monroy

Sao Paulo, April 6, 2014

 

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