The obscure game-theory problem that explains why rich countries are rich.

The economic mysteries of daily life.
Sept. 28 2007 3:10 PM

The Stag Hunt

The obscure game-theory problem that explains why rich countries are rich.

Rabbit. Click image to expand.
We are hunting wabbits ...

As the lines formed down the street outside branches of the troubled British mortgage lender Northern Rock last week, it was obvious enough to a game theorist what was going on: People had decided to hunt rabbits. Bear with me—this will make sense in a moment.

Game theory is the study (by economists, mathematicians, biologists, and others) of situations in which what you do may affect what I choose to do, and what I do may affect what you choose to do. The theory is big on catchy stories with memorable names, but ultimately it is all about mathematical representations of interactive decisions, called "games." The most famous game of all is the "prisoner's dilemma," in which two prisoners must each decide whether to plea-bargain by giving evidence against the other.

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But another game, the "stag hunt," languishes in relative and undeserved obscurity. In the stag hunt, two hunters must each decide whether to hunt the stag together or hunt rabbits alone. Half a stag is better than a brace of rabbits, but the stag will only be brought down with a combined effort. Rabbits, on the other hand, can be hunted by an individual without any trouble.

There are two rational outcomes to the stag hunt: Either both hunters hunt the stag as a team, or each hunts rabbits by himself. Each would prefer to cooperate in hunting the stag, but if the other player's motives or actions are uncertain, the rabbit hunt is a risk-free alternative.

Northern Rock's customers have decided to hunt rabbits. If they had confidence that other depositors would stay with the bank, there's not much doubt that their money would be safe. When they lost that confidence, the stag hunt was abandoned. And despite all the talk about panic, it was abandoned for perfectly sensible reasons.

The stag hunt is inspired by an anecdote originating with Jean Jacques Rousseau about a deer hunter abandoning his post to chase a hare. Yet it is more than an offbeat parable about cooperation. In the hands of economists, it becomes a mathematical object that can be pulled apart and tested to see how it works. One worrying outcome of that research is the discovery that it is very hard to move from the low-trust situation, in which each hunter chases his own rabbits, to the more trusting situation, in which both team up to bring down the stag. Any move to the high-trust equilibrium is going to require its own, possibly costly, attempt at coordination.

Perhaps we should not be surprised that trust is difficult to regain once lost.

Human society is full of stag hunts, but richer societies have become very good at formalizing the cooperative outcome. I can walk into a shop, pick up something expensive, and then walk out with it without handing over any cash. I use a credit card: The shop assistant does not know whether to trust me, but she trusts the credit card company, and they trust me.

That is a formalized form of trust, based on institutions that dramatically expand our ability to interact with those beyond our immediate neighbors. Economists who study such things—such as the World Bank's Steve Knack, or Paul Seabright, author of The Company of Strangers—argue that the difference between countries that have successfully formalized trust and those that have not is, basically,  the difference between rich countries and poor ones.

That is why the stag hunt is so important, and the fragility of the happy, cooperative hunt is so worrying. Britain is not about to collapse into anarchy, even if the experience of Northern Rock's depositors is profoundly unnerving. But the episode is a reminder of how many conventions in our society—from lining up to showing up for work—only succeed because everybody expects that they will. That cannot be taken for granted.

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