Thursday, April 9, 2009

The Prisoners' Dilemma and the Role of Government

You can read the metaphoric version of this game here. Simplified, these are the rules:

You and another guy are playing a game. You each have two buttons in front of you, a red one and a green one, and you each get to push one button once with no opportunity to know or influence the other's choice. The choices you each make will determine the pay-off.

  • If you both push Green, you each get $2
  • If you both push Red, you each lose $5
  • If you each push different buttons, the one who pushes Red gets $10 and the other loses $12.
What do you do?

First, I hope, you compare the possible outcomes for each choice you can make:
  • If you push Green, you get $2 if the other guy pushes Green or you lose $12 if he pushes Red.
  • If you push Red, you get $10 if the other guy pushes Green or you lose $5 if he pushes Red.
Note that your pay-off for pushing Red is better than the pay-off for pushing Green, whatever the other guy does. But note also that the combined pay-off for both players is either zero or negative unless you both push Green. So, your best strategy is to push Red, but the strategy that is best for “the team,” if you are a team, is for you both to push Green. But you are not a team under these rules.

So let's change the rules. Under the new rules, you don't play only once. You play repeatedly. Now there's something in it for you to cooperate by pressing Green together. You could reliably earn $2 a round. Yes, you could earn $10 by defecting, but if you do, trust is lost, and the opportunity to continue to earn those $2 bills ad infinitum goes away. That's a heavy price to pay for one quick score.

Well, zillions of pages have been written about this little game, because virtually all of civilization runs on it. The Prisoners' dilemma is a “plus-sum” game: if the players cooperate, they come away with a combined win. Those $4 victories make peace an asset and prosperity possible. Those victories are why, if we cooperate, our lives need not be solitary, poor, nasty, brutish, or short.

Of course, real life is messier than parlor games, but the simple game described above can be restructured to map some important real world situations. Suppose that if the players push different buttons, the guy who pushes Red gets $100,000,000, and the guy who pushes Green is killed (and so the game does not repeat), the women he loves are raped, and his children are sold into slavery. Not much point in pressing Green in that game. But now add that one player can arbitrarily force the other to press Green while the former pushes Red. We can call this game “Darfur.”

What if you don't know that the game is on or where the buttons are, or that someone has surreptitiously placed a green button where you will inadvertently press it as he lies in wait to press Red and abscond with his winnings. You may not even know your $12 is missing, or if you do, you don't know who has the $10 prize. We can call that game “Burglary.” Or maybe “Madoff.”

But there are plus-sum games to be played, where pressing Green means nothing more than not doing any of the things that we generally treat as crimes. It turns out that merely respecting the person and property of others is all it takes for the $2 bills to start rolling in, as people organize enterprises on the assumption that they will be able to bring them to production, sell their output, and keep their profits.

What we need is to be sufficiently confident that no one will play Darfur with us and that too few people will play Burglary or Madoff to matter. How do we do that? The answer, in a word, is government. Not necessarily “Leviathan,” but government – an organization with a monopoly on the legitimate use of force, with the mandate to use that force to assure, and only to assure, that external enemies do not play Darfur with us, and internal enemies do not play Burglary.
That's what governments are constituted to do. How else do we secure the blessings of liberty to ourselves and our posterity?

I am not arguing that national defense and law enforcement are the only activities in which government can engage. Public education, for example, creates a populace capable of earning those $2 bills and thus not tempted by some less salutary game. Public health makes the playing field safe for the players. These are just two examples of the things government can do to protect the standard iterated plus-sum game that we call civilization. Obviously, there are others, the merits of which are sometimes apparent and sometimes not.

So, when analyzing public policy, I suggest that the question to ask is simply “Is this good for the game?” If it helps the game, it's a good idea; if it doesn't, it isn't.

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