Guessing games

To compute the proper strategy without game theory requires you to guess the other players' strategies. That doesn't seem so bad, but it's hard to deal with mathematically. Any game, indeed any interaction with other people, involves incalculable risks. That should make you uncomfortable and discourage you from playing. Always keep in mind the idiot in the horror movie who finds the old scroll with the spell for summoning demons and decides to see whether it works. What's going to happen to him is an important object lesson in incalculable risk. If you do decide to play games anyway, don't invent a fantasy world in which the risks can be calculated.

One problem with game theory is that people don't behave the way it suggests. Extensive experiments have turned up many systematic deviations from optimal game theory behavior, but very few examples where people use it. It's true that under the assumptions of game theory you don't have to worry about that (one telltale danger sign for a theory is that proponents tell you it doesn't matter whether it's true). Your game theory strategy is optimized against the best possible strategy your opponents can choose from their point of view; if they choose anything else, you will do at least as well. But since your opponents often won't choose that strategy, a simpleminded person would say that you are walking around with a shield for a weapon nobody has. Game theorists dismiss that criticism because the simpleminded critic is too dense to follow the math. But you can't ignore dense people-they're not unarmed; they're armed differently. It hurts just as much to be hit by a stupid person as by a smart one. A second problem is that game theory often gives demonstrably wrong answers, even in the simplest games. The most famous example is the prisoner's dilemma. Two criminals are arrested fleeing a failed bank robbery. Unfortunately for the police, none of the witnesses can identify them as the robbers, and there is no other physical evidence. Both of the criminals can be convicted of resisting arrest, which carries a sentence of 1 year in prison. A conviction for attempted bank robbery carries a 10-year sentence. The criminals are separated and each is offered the same deal: Inform on your partner and go free. But if both criminals confess and inform, each will get a 9-year sentence-1 year off for informing.

If one of the criminals is a game theorist who turned to robbing banks after losing all his money playing poker against players too dumb to understand the theory, he will always confess. He'll reason that whatever his partner does, he saves 1 year in prison by confessing. If his partner remains silent, the game theorist goes free instead of serving 1 year. If his partner rats him out, the game theorist gets 9 years instead of 10. So he confesses. His partner, cursing himself for trying to rob a bank with a game theorist, confesses as well. He's not going to get stuck being loyal to a guy who doesn't understand loyalty. So both of them serve 9 years, when less mathematically sophisticated crooks are out in a year. It would be cruel and unusual punishment to put them in the same cell: Imagine 9 years of your cell mate explaining how smart you both are to be there.

There is no problem with the mathematics here; it's entirely selfconsistent. The conclusion follows inexorably from the assumptions. I'm also not criticizing the game theorist's decision to confess, since his partner did the same thing for different reasons. The problem is the game theorist's initial characterization of his partner as an opponent. Once that happened, trust, loyalty, and cooperation were meaningless. This was a one-shot game against a faceless opponent, not a step in a human relationship or a business enterprise. The recommended action would be the same if the partner were the game theorist's best friend or worst enemy-in fact, the terms friend and enemy become meaningless. Everyone is an opponent-not a vindictive opponent; just a decision-making entity maximizing its own utility function without regard for your welfare.

It's easy to see how this kind of thinking poisons international diplomacy. Everyone is an opponent, and you prepare for their most harmful strategies. This applies to friendly and unfriendly countriesfor that matter, it applies to domestic politics as well. It is sound military doctrine to "prepare for your enemy's capabilities, not his intentions," but it applies only to enemies. It's crazy to treat everyone as an enemy. Worse, it will cost you money in poker. There is more cooperation than competition at a poker table, but some game theorists can't see that. It applies with even more force in finance.

I am not against game theory; it is a useful tool for understanding some aspects of poker. And I'm not against people who study it; there is brilliant and important work being done in both theoretical and experimental game theory. My criticism is reserved for people who understand the basics, then think they understand everything. I want to play poker with these people, but not rob banks with them.

Дата добавления: 2015-10-26