Stag hunt
In game theory, the stag hunt is a game that describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, they must have the cooperation of their partner in order to succeed. An individual can get a hare by themself, but a hare is worth less than a stag. This has been taken to be a useful analogy for social cooperation, such as international agreements on climate change.
The stag hunt differs from the Prisoner's Dilemma in that there are two pure strategy Nash equilibria: when both players cooperate and both players defect. In the Prisoner's Dilemma, in contrast, despite the fact that both players cooperating is Pareto efficient, the only pure Nash equilibrium is when both players choose to defect.
An example of the payoff matrix for the stag hunt is pictured in Figure 2.
Formally, a stag hunt is a game with two pure strategy Nash equilibria—one that is risk dominant and another that is payoff dominant. The payoff matrix in Figure 1 illustrates a generic stag hunt, where . Often, games with a similar structure but without a risk dominant Nash equilibrium are called assurance game. 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.
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