Stag hunt

In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Rousseau described a situation where two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. If an individual hunts stag, she must have the cooperation of her partner. An individual can get a hare by herself, but a hare is worth less than a stag.

An example of the payoff matrix for the Stag Hunt is as follows:

A Stag Hunt has also been considered by David Hume in his discussions of the social contract.

Formal definition

Formally, a Stag Hunt is a game with two Nash equilibria one that is risk dominant another that is payoff dominant. The following matrix illustrates a Stag hunt, where a>b>=d>c.

Often, games with a similar structure but without a risk dominant Nash equilibrium are called Stag Hunts. For instance if a=2, b=1, c=0, and d=1. While (Hare, Hare) remains a Nash equilibrium, it is no longer risk dominant. Nonetheless many would call this game a Stag Hunt.

The Stag Hunt and social cooperation

Although most authors focus on the Prisoner's Dilemma as the game that best represents the problem of social cooperation, some authors believe that the Stag Hunt represents an equally (or more) interesting context in which to study cooperation and its problems (for an overview see Skyrms 2004).

References

Skyrms, Brian. (2004) The Stag Hunt and Evolution of Social Structure Cambridge: Cambridge University Press.

External links

• The Stag Hunt at GameTheory.net