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A beautiful idea?

from David Ruccio

What most of my students know about  and game theory (at least before sitting through my two or three lectures on the topic or taking an entire course in game theory) they derived from the film, A Beautiful Mind, and the stupid example used to illustrate game theory in the film (of a blond woman walking into a bar).

As Kenneth Chang explains, the episode in the film is not an example of a Nash equilibrium.

A simpler example is what is known as the Prisoner’s Dilemma. Two conspirators in a crime are arrested and offered a deal: “If you confess and testify against your accomplice, we’ll let you off and throw the book at the other guy — 10 years in prison.”

If both stay quiet, the prosecutors cannot prove the more serious charges and both would spend just a year behind bars for lesser crimes. If both confess, the prosecutors would not need their testimony, and both would get eight-year prison sentences.

At first glance, keeping quiet might seem the best strategy. If both did so, both would get off fairly lightly.
But the calculation of the Nash equilibrium shows they would likely both confess.

This type of problem is called a noncooperative game, which means the two prisoners cannot convey intentions to each other. Without knowing what the other prisoner is doing, each is faced with this choice: If he confesses, he could end up with freedom or eight years in prison. If he stays quiet, he goes to prison for one year or 10 years.
In that light, confessing is the better option. And he knows that the other prisoner has the same incentive to confess, so it is less likely he would stay quiet.

Further, changing strategy to staying mum would be a bad move — longer prison term — unless the other prisoner somehow also decided to do that. Without any communication, that would be a highly risky guess, and thus, this strategy represents a Nash equilibrium.

When I teach game theory, I use a couple of other examples to illustrate the problems highlighted by game theory.

One, in the area of noncooperative games, has to do with the wages paid by capitalist employers: they want to pay their own workers low wages (to extract as much surplus as possible) but they want the workers of all other capitalists to be paid high wages (so they can purchase the commodities being produced). This is one of the basic contradictions of capitalism. These days, the noncooperative solution—even in the midst of declining unemployment—is to keep the wages of most workers low.

The other is the so-called ultimatum game, which, in the simplest form of the ultimatum game, involves a proposer who decides how much of a sum of money (say, $10) to give a responder, and the responder decides whether to accept or reject the offer. If the responder accepts, the players split the money in the way the proposer suggested. If the responder rejects, neither player gets any money. The neoclassical version of game theory predicts that, since both the proposer and the responder know that rejection of the offer results in neither receiving any money, the proposer will offer the smallest possible amount (anything greater than $0) and the responder will always accept. As it turns out, during actual experiments, participants choose outcomes that are much closer to a 50-50 split, which runs counter to the usual notion of self-interest—something we might call “fairness.”

But there’s an additional—to my mind, quite beautiful—outcome due to Robert H. Frank, Thomas Gilovich, and Dennis T. Regan: economists and students who have taken courses in neoclassical economics are much less likely to engage in cooperative behavior than noneconomists and students who have not been exposed to those ideas.

  1. May 27, 2015 at 5:47 pm

    I have seen the movie ” A Beautiful Mind” and have seen an interviewer desperately trying to make an interview with Nash interesting. He failed.
    Not to say anything against the person Nash, but the adoption and glorification of his ideas on game theory as being fundamental to economic behaviour, surprised Nash more than anybody else, I believe.
    His ideas were used to justify the current casino mentality in the financial system which is now wreaking havoc with our economies.

  2. May 27, 2015 at 6:08 pm

    Yes, they are more selfish because they are being fed dubious ideas about how people strategise with one another that is far more cynical than what happens in real life. Using that same ideology to teach left-wing ideas is just as poisonous as using it to teach right-wing ideas.

  3. May 28, 2015 at 9:19 am

    Maybe economists are more selfish because those who select such profession have the feature in the beginning. Just wondering

  4. Kihano
    May 28, 2015 at 10:51 am

    Game theory is inaplicable to economics or any other social area. Thus, there is no need to be included in the economics students programs.

  5. Nell
    May 28, 2015 at 1:58 pm

    Joseph Heinrich (UBC Vancouver, I think) has done some interesting cross-cultural work on the ultimatum game. His research suggests that how people behave in the game is determined by socio-cultural factors not innate properties of human behaviour. Thus any generalizations of human economic behaviour from studies like the UG and prisoner’s dilemma are inevitably going to be undermined by people’s actual behaviour. For example the 50-50 split on the UG is thought to be associated with market-based economies where ‘fairness’ in exchanges is necessary for market exchanges. Presumably, once people begin to believe that market players are in it to rip them off, it becomes a lot more difficult to increase or expand market exchanges. Possibly another nail in capitalism’s coffin, as more and more people have come to distrust the market?

  6. Ack Nice
    May 28, 2015 at 2:10 pm

    On the ultimatum game; I think that game isn’t about morals, it’s simply an intelligence test. If I am the absolutely greediest, most self-interested person in the world who doesn’t care one lick about you and your prosperity, I’m going to offer you a 50-50 split every time without hesitation because that is the only move that *guarantees* I get the maximum money every time…and, again not caring a lick about what happens to you, but only caring what happens to me, with the 50-50 split I effortlessly make a friendly-feeling person who wishes me no harm instead of creating resentfulness that will lurk in my environment, waiting to get back at me the first chance that comes around to the person I inferiorized.

    People’s sense of justice is very, very strong. It never dries up and goes away. (Studies have shown that even dogs have a sense of justice and resent and react to being treated unjustly. Rover notices if Fido gets all the cookies and discord in the pack results.)

    Equality breeds no strife. Injustice drives violence.

    Serious question: Has any responder *ever* refused a 50-50 split?

    Offer ME 49% and you’ll get $0 and buy my everlasting resentment for your insult.

    Fairness IS self-interest! Pursue your maximum happiness with all mindfire! Minimizing wealthpower inequality as far as is possible gives 100% of people the happiest possible planet to live on. And isn’t that what it’s all about – whether you’re an economist or a ditch-digger??

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