Chocolate and Gold Coins

Tuesday, July 05, 2005

The Problem With Game Theory

This is a continuation of this post on the Five Pirates Game. I want to illustrate a problem with a conventional viewpoint of game theory. I can do that just as easily with a simpler game: The three pirates game. There are 60 gold coins to be divided by 3 pirates. Pirate 1 gets to suggest an allocation, for example 60,0,0 or 20,20,20. Pirates 1,2, and 3 vote. If two out of three vote against the allocation, pirate 1 gets nothing and pirate 2 decides how to split the 60 coins.

In this simplified game, we will assume that the pirates only care about themselves (so they have no bad feelings about gypping their fellow shipmates) and are intelligent. Pirate 3 knows that pirate 2 will 1) vote against anything that pirate 1 proposes, and 2) will give himself all 60 coins if he gets the opportunity. Therefore, pirate 3 simply accepts whatever pirate 1 gives him – if he gives him anything. So the allocation is 59,0,1.

There are several potential objections to this reasoning:
1. These pirates have to work together over time. It makes no sense to rip each other off.
2. Pirate 2 and 3 just need a lawyer to draft up an agreement (perhaps a 50-50 split) and then the outcome changes completely.
3. Pirate 2 can increase his payoff if he can convince pirate 3 that he (pirate2) is an oddball who cares little about money and just wants pirate 3 to have it all (how he could do this is an open question).
4. Its worth a gold coin to deny the scoundrel pirate 1 the 59 coins that he gives himself.

All of these objections could be valid in some sense, but they miss the real issue.
1. These pirates many not be playing a repeated game – this might be the last voyage and they will go their separate ways.
2. There probably aren’t any lawyers around, and the courts won’t be their allies anyway.
3. Pirate 2 might be simply unable to convince pirate 3 that he is an oddball – pirate 3 knows the other crew pretty well by now.
4. If pirate 3 is emotional, pirate 1 might be too greedy in offering only one gold coin, but we don’t know that pirate 3 is emotional and irrational.

I think that pirates 2 and 3 do not need a lawyer: they just need a handshake. If pirate 2 agrees to give pirate 3 half of the booty, then probably pirate 3 will take the chance and vote down 59,0,1. I think it would be surprising if the allocation were anything other than 20,20,20 because its fair, and there is honor among thieves. Thievery would have made itself extinct long ago if thieves act so unethically among each other. People who work together automatically create ethics that bind them to agreements; they don’t need lawyers.

The central problem with non-cooperative game theory is that it implicitly ignores ethics, and therefore, it explicitly ignores human’s instinctual method of avoiding the pitfalls of non-cooperation. Sure, some people, including pirates, are unethical, but usually this unethical behavior stems from people being unethical (or at least appearing to be unethical) to them. Co-workers seldom feel that way with each other because otherwise they wouldn’t be co-workers.

What is ethics? I would define it as a rule which, if violated, would cause self-punishment for the violator. So if pirate 2 is unethical and keeps all of the gold, his conscience will bother him so much that he will find no pleasure in his 60 gold coins. If pirate 3 knows that pirate 2 is ethical, he can trust him, and pirate 2 actually makes more money than if he had been both greedy and without conscience. It is important to note that this ethical rule doesn’t help pirate 2 in all cases: if he stumbles upon some wealth, he might feel ethically obliged to share with his buddies, even though he would like to keep it all. This might pay off for pirate 2 later (this is how pirate 3 knows he can trust him) but he doesn’t know for sure it will ever pay off for him.

Why would ethics occur at all? Why would we want to punish ourselves? The point is that we don’t choose ethics, ethics choose us. Our parents raise us to be good people, and we simple obey them by instinct. And an ethical instinct helps people avoid the pitfalls of non-cooperative game theory (and lets us get 20 gold coins instead of 1).

Ethical behavior is only likely to emerge among small groups of people who work closely together or with professional organizations like the ABA. Admittedly, it is hard to tell the difference between ethical behavior and being overly optimistic in playing a repeated game, except when someone does something extreme like falling on a hand grenade. In that case, the non-cooperative game theorist would think he is just a poor game theorist (since he died) but that’s just a judgment.

Ethics dies when people have to act on behalf of their group. Their loyalty is to their own group and not to other groups. A corporate manager has to look out for the good of the company; doing the “right thing” is meaningless in this context. Therefore, non-cooperative game theory might be a good way to explain corporate behavior.

The good news for companies is this: they never lack lawyers!


  • People instinctually get along and cooperate, but people ALSO instinctually cheat to get ahead.

    After reading Freakonomics and thinking about the issue, I've concluded that there's a lot more cheating going on than we like to think there is.

    By Anonymous Half Sigma, at 10:39 AM  

  • " People instinctually get along and cooperate, but people ALSO instinctually cheat to get ahead."

    And some people will punish unethical people at their own expense.

    Economists have been interested in why such people are there and if they are necessary. It turns out that they are absolutely necessary for a cohesive group.

    I no longer remember the details but this economic experiment was discussed in the Economics Focus section of the Economist magazine a long time ago. I don't have access to the internet archive or the old magazines. If any one of you have you should check it out.

    yum yum

    By Anonymous Anonymous, at 12:14 PM  

  • Hi Half-Sigma and Yum Yum
    It makes a big difference if you can cheat and not be detected and if you can cheat but have to take the heat from the cheated. Even in that latter case, however, lots of people would feel bad about cheating someone for no good reason. Think about the last time you went to a restaurant that you left thinking "I'm never coming back here again." Did you leave a tip?

    By Blogger Michael Higgins, at 1:48 PM  

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