Stag hunt

In game theory, the stag hunt, sometimes referred to as the assurance game, trust dilemma or common interest game, describes a conflict between safety and social cooperation. The stag hunt problem originated with philosopher Jean-Jacques Rousseau in his Discourse on Inequality. In the most common account of this dilemma, which is quite different from Rousseau's, two hunters must decide separately, and without the other knowing, whether to hunt a stag or a hare. However, both hunters know the only way to successfully hunt a stag is with the other's help. One hunter can catch a hare alone with less effort and less time, but it is worth far less than a stag and has much less meat. It would be much better for each hunter, acting individually, to give up total autonomy and minimal risk, which brings only the small reward of the hare. Instead, each hunter should separately choose the more ambitious and far more rewarding goal of getting the stag, thereby giving up some autonomy in exchange for the other hunter's cooperation and added might. This situation is often seen as a useful analogy for many kinds of 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: one where both players cooperate, and one where 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 games. For instance if a=10, b=5, c=0, and d=2. While (Hare, Hare) remains a Nash equilibrium, it is no longer risk dominant.