Stag Hunt

The stag hunt is a two-player game in game theory in which each player must choose, without knowing what the other will choose, between cooperating to hunt a stag, which yields a large payoff to both but only if both players commit to it, or acting alone to hunt a hare, which yields a smaller but guaranteed payoff regardless of what the other player does. The game takes its name from a passage in the eighteenth-century philosopher Jean-Jacques Rousseau's Discourse on Inequality, describing two hunters who must decide whether to cooperate on a stag hunt or defect to catch a hare individually, though Rousseau himself did not formalize it mathematically; the game-theoretic version was developed and named after his example in the twentieth century. Unlike the more widely known prisoner's dilemma, the stag hunt has two distinct stable outcomes, called Nash equilibria, one in which both players cooperate and one in which both act alone, so that the central difficulty the game illustrates is not a temptation to individually defect but the risk of trusting a partner to cooperate when a failure to coordinate leaves the more cautious, individually safe choice looking preferable. Because of this structure, the stag hunt is used across economics, political science, and evolutionary biology as a standard model of situations where mutual cooperation is better for everyone but requires trust that is not always rational to extend, contrasting with the prisoner's dilemma's very different incentive to defect even when both would benefit from cooperating.