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The poisoner's dilemma
March 23, 2010 - 4:56pm

I was reminded recently of the classic game theory scenario known as The Prisoner's Dilemma. It goes something like this:

You and another person have been arrested on suspicion of a serious crime. The cops can definitely hang a smaller rap on you, but they desperately want a confession because their case on the main charge is weak. You and your alleged accomplice are being held in separate cells, with no opportunity to communicate. The deal laid out to you is as follows.

If you confess and your accomplice doesn't, you walk free and the other guy gets 10 years in prison. If he confesses and you don't, he goes free and you get the 10 years. If you both confess, you each get 7 years. If neither one of you confesses, the cops won't be able to make the main charge stick; you each should be out in 6 months.

What do you do?

Game theory typically assumes that each actor is motivated by self-interest. Early, simple, approaches presume perfect information and no complications like trust issues or misleading impressions of other players -- later versions of game theory are more subtle. But The Prisoner's Dilemma is from the early days, so actor motivations are assumed to be pretty simple.

You're faced with only one choice -- confess or not. If your accomplice confesses, you're better off confessing, too. (Your ten year sentence gets cut to seven.) If your accomplice doesn't confess, you're still better off confessing. (Your six months entirely disappears.) But because each of you is better off confessing -- given no knowledge of the other person's decision -- you each end up serving seven years when you could have gotten out in six months.

What brought this to mind? Thinking about the likelihood of meaningful international climate accord. If all countries act decisively to minimize climate change, all countries benefit. If no country acts, all countries suffer. If only some countries act, all countries suffer climatically, and the ones who acted also suffer economically.

National governments are being asked to make potentially momentous decisions which, depending on what other nations do, can seriously advantage or disadvantage them in future. And the biggest decisions come with the largest budgets and the longest lead times, and so must be made in imperfect knowledge of whether the other players will really cooperate or not.

Nations are in slightly better position than hypothetical prisoners because each nation at least knows what the other ones say they're willing to do. But confidence in the international community (sic) is low, and what a country says it's going to do has become as much of a negotiating point as what it really ends up doing.

Moreover, the costs (and hence risks) of taking action are in the (monetary) units governments best understand, and success (in terms of international politics) is defined more in relative than absolute terms. (Governments get rewards at least as big for doing better than the other guy as they get for doing well.)

Like prisoners held incommunicado, national governments find themselves in a situation where simple self-interest can lead us all to a grossly sub-optimal result. So either we need to find some way to get global action that's not in the form of treaties among national governments, or we need to develop different versions of individual/national motivation.

And more advanced game theory.



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