THE STAG HUNT

THE Stag Hunt is a story that became a game. The game is a prototype of the social contract. The story is briefly told by Rousseau, in A Discourse on Inequality: “If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple.” Rousseau's story of the hunt leaves many questions open. What are the values of a hare and of an individual's share of the deer, given a successful hunt? What is the probability that the hunt will be successful if all participants remain faithful to the hunt? Might two deer hunters decide to chase the hare?

Let us suppose that the hunters each have just the choice of hunting hare or hunting deer. The chances of getting a hare are independent of what others do. There is no chance of bagging a deer by oneself, but the chances of a successful deer hunt go up sharply with the number of hunters. A deer is much more valuable than a hare. Then we have the kind of interaction that is now generally known as the stag hunt.