Who lacks rationality? October 8, 2006 | 09:01 am

Why say no to free money? It’s neuro-economics, stupid

While it’s gratifying that economics is finally getting past the idea of man as a simplistic economic creature, I don’t think either the economists or the physcologists (two groups that, in general, are not known for their astute logic) have thought the matter through. I’d argue passing up free money can be logical. It’s all in how often the game is played.

Ultimatum is just one of the many variants of the prisoners dilemna that have shown up over the years. For those who haven’t read Douglas Hofstedter’s glorius “Metamagical Themas”, I’ll recap here (although, without a doubt, go buy and read the book, and “Godel, Escher, Bach” as well). Let’s say you want to buy something illegal from someone you don’t really know- drugs, diamonds, military secrets, whatever. The two of you hit upon the following scheme. You’ll put the agreed upon money in a brown paper bag, and he puts the diamonds (or whatever) in one as well. Then, over lunch tomorrow, you’ll sit on the same park bench, “casually” putting your brown paper bags beside each other. But when you or he get up to leave, instead of taking your own paper bag, you take his (no peeking!). Then you’ll both walk away and never see each other again.

You now have a choice. You can choose to either cooperate, and put real money in your paper bag. Or you can choose to defect, and put cut up newspapers instead. He won’t be able to tell one way or another until it’s way too late. Likewise, he’s facing the same decision. He could put diamonds in his paper bag (cooperate), or just gravel (defect), and there’s no way for you to know until it’s way too late. Which do you do?

If it’s a one time thing, the only rational (for a purely selfish economic point of view) is to defect. You may get lucky, and get a bag full of diamonds for free. Or you may just get a bag full of gravel, but at least this way you won’t be out the money. But let’s make it more interesting. Instead of a one off deal, you plan to do it every working day for a month- 20 times, you’ll meet at the park bench and exchange bags. But now, you have more information- you have a history. You know, for all the previous days, wether he’s given you a bag full of diamonds or a bag full of gravel. And he’ll know wether you’ve given him real money or cut up newspapers.

Hofstedter was part of an experiment on this game back in the early eighties. A large number of mathematicians and programmers were invited to submit algorithms. All the algorithms would be played against each other, for 20 rounds (building up a history). If both algorithms decided to cooperate, they’d both win 3 points. If one defected and the other cooperated, the defector got 5 points and the cooperator 0. If both defected, both got 1 point. When all algorithms had played all other algorithms, the algorithm that had scored the most points over all games was the winner. The game was seeded with a number of simple algorithms, and rather surprisingly, one of these won- a strategy known as “tit for tat”. It was very simple- it always cooperated on the first round, and on all succeeding rounds, it simply did whatever the other algorithm did last round. If the other algorithm defected on rount n, tit-for-tat would defect on round n+1. The second year, new algorithms were invented, and the game ran again- and again tit-for-tat won, despite there being several algorithms explicitly designed to detect and “beat” tit-for-tat. The third and final year, tit-for-tat won again.

The third year, the game was played a second way, to see if Darwinian selection changed the game. All surviving algorithms played all other surviving algorithms every “generation”. An algorithm that performed above average got more copies of itself in the next generation. An algorithm that performed below average got fewer, or even none. This actually magnified the advantage of tit-for-tat (and other algorithms that tended to cooperate) even more, as the more copies of tit-for-tat there were, the more successfull tit-for-tat was.

Here’s the important lesson. Repeating the game, and building up a history, changes the nature of the game- cooperation becomes a viable, even superior, strategy. Tit-for-tat has three interesting properties: 1) it encourages cooperation by (initially) being cooperative, 2) It discourages defecting by punishing defections, and 3) it allows for the other player to regain it’s trust (it’s forgiving). Having these virtues is, in a very real sense, a pro-survival characteristic, even in the real world. Humans do better cooperating in groups than we do on our own. A group of humans is both much better off, and much more likely to survive, as a group than as individuals. Even in the modern “anonymous”, world- how often do we have multiple contacts, multiple exchanges, with the same entities? Ask any non-chain restaurant owner- repeat business is where the money is. Heck, that’s true of any business, it’s just that some businesses are well enough off that they can kind of afford to forget it. Most economic transactions are more similiar to the multi-round prisoners dilemna than they are the single-round (original) version. It makes sense that our emotions, our “pre-programmed logic”, tends to assume the multi-round version of the prisoners dilemna, because that’s by far the most common case.
Now, let’s look at this ultimatum game as a variant of prisoner’s dilemna. The other person can choose to cooperate, and give you your “fair share”, or he can choose to defect, and give you less. You can choose to cooperate, and take what you’re given, or defect, and not. If it’s a one round game, pure logic says you should always take what you’re given. But what if it’s a multi-round game? Now the logic changes. And the $2.50 mark is an interesting mark. Say it’s a two round game. In the first round, the other player offers you $2. If you take it, the other player has *no* incentive to offer you more than $2 in the second round. And they might offer you less. So you maximum take for both games is going to be $4. On the other hand, if you don’t take the $2, and punish the other player for not being fair, it’s signifigantly more likely that in the second round they will be fair. A likely offer would be $5 on the second round, splitting the take 50/50. In fact, any offer above $4 is a net win- you end the game with more money than you would have if you had accepted the $2 in the first round. By the selfish logic of the economist, it makes sense to decline the free money in the first round.

This is a problem I seem to routinely have with many economists. Logic is like a machine- it works on false premises as well as true ones- however, given false premises it produces false results. GIGO- Garbage In, Garbage Out. Simply because your logic is flawless doesn’t necessarily mean your results are correct, if you start from flawed premises. And this seems to be endemic with economists. Employees and Customers are not distinct groups of people (especially not on the macro level). Prisoner Dilemna style games are not generally single-round, but generally multi-round or even open-ended (unlimited number of rounds). And so on.


  • DavidM

    Sorry you have economics confused with smuggling. The problem with this type of thinking(only one person wins) is that it only considers the moment and not the future.

    Logically as a consumer I don’t *want* to shortchange a business who is providing me goods or a service. As a matter of fact, I will gladly pay for any service or product I enjoy.

    As a business if I shortchange my consumers I won’t expect to stay in business very long; as a matter of fact others will most likely notice my poor service and start a business to take all my customers.

    The number one rule of a free market: you cannot make money without helping people.

    The problem with splitting things ‘fairly’ is that it does not encourage *anyone* to take any risks. And why should they if all they can expect is a ‘fair’ cut? Progress is built on people taking risks and they should expect big rewards for doing so. Thus far history has borne this out: South Korea has a bigger economy than all of China!