Sunday, November 8, 2009

The Stag Hunt

Last week I was at the local grocery co-op buying some avocadoes and tomatoes. At the checkout line, the cashier, a Jamaican man with dreads, started making some small talk. What do you major in, he asked. Oh, economics? Hey, what do you think of the Fed?

I don't know much about the Fed, really, so I said I didn't wade much in political debates (which I don't) and that I thought they employed decent enough people. I prefer going through life assuming the best in people, assuming that the world isn't rigged against me, I said. The Jamaican man turned serious: But sometimes things are rigged. Sometimes things are rigged, and you have to fix them.

Hm. In my conversation with the Jamaican man, I got the sense that he believed things (the economy, the state of the world, etc.) were messed up only because someone was there to mess it up; that he felt that if only people were cooperative (i.e. "give peace a chance"), the world would be a great place. And this seems a really natural position to take, since, after all, our problems are human-made. But it turns out that our society doesn't work like that. The startling and fascinating conclusion of game theory is that we can end up in sub-optimal outcomes even if everyone would like to cooperate.

How is this possible?

The story behind the game goes back to Rousseau. Imagine, he said, a group of primitive people who had a choice between hunting stag and hunting hare. Hunting stag would, of course, be the best option because it would yield lots of rich meat, but the problem is that it requires everyone to work together to take the stag down. On the other hand, they could hunt hare individually, but the reward wouldn't be as great. In game form the story looks like this:

The numbers in the boxes represent how the players (in this case, an individual vs. the rest of society) value the outcome. Thus everyone hunting stag is the best outcome (3), both hunting hare is second (2), and getting screwed is the worst (1), because you not only waste your time running after the stag, but you don't even get any food.

In other words, these people are as cooperative as you're going to get: They would like to work together and they don't like to take advantage of each other. And yet it's still possible for these primitive people (and us possibly less primitive people) to get stuck in a Hunt Hare/Hunt Hare equilibrium!

The catch here is that it matters not just what players want to do, but what they think others will do. Everyone would like to hunt stag, but only when everyone else hunts stag. So if people think others are inclined to cooperate, they'll cooperate too; but, on the flipside, if everyone is scared of getting screwed over, then they're likely to not cooperate.

Notice that the basic fact that all these people are cooperative hasn't changed. It's just that they don't know that they're all cooperators. And this uncertainty causes all the problems: cooperation is risky, it leaves you vulnerable, and people aren't willing to gamble too much. [Indeed, this game is also called an Assurance Game, because if players were assured that the other was a cooperator, then they would cooperate too.]

This is my long comment to the Jamaican man's remark. Yes, Jamaican man, sometimes things are rigged. But sometimes we can end up in all sorts of social problems even when no one is at fault.

For more information on the Stag Hunt and cooperation and such, see Brian Skyrms' book: The Stag Hunt and the Evolution of Social Structure.

1 comment:

  1. One note: A senior economics major did some research on the Fed recently with my advisor, an economics professor, and they found that (after looking at a bunch of transcripts from Fed meetings), although the Fed's job is to balance their time between combating unemployment and keeping inflation under control, they almost NEVER discussed unemployment.

    The idea is, of course, that inflation inflicts far worse damage overall on the wealthy than it does on the poor or middle class.

    Just something to chew on.