Stag Hunt

The Stag Hunt is a coordination game in which two hunters can cooperate to hunt a stag (yielding a high payoff for both) or defect to hunt a hare (yielding a moderate payoff for the defector and nothing for the cooperator who trusted them). Unlike the Prisoner's Dilemma, the Stag Hunt has two pure-strategy Nash equilibria: mutual cooperation (stag, stag) and mutual defection (hare, hare). In the standard formulation, the mutual stag equilibrium is both payoff-dominant and risk-dominant — a rare alignment of efficiency and security that makes the Stag Hunt the game theorist's favorite model for how social trust and cooperative institutions can emerge without centralized enforcement.

The game is named after Rousseau's parable in the Discourse on Inequality, and it is also known as the Assurance Game because the core strategic problem is assurance: each player needs to trust that the other will cooperate, not merely to avoid being exploited but to avoid the catastrophe of unilateral cooperation. The Stag Hunt thus captures a form of trust that is deeper than the tit-for-tat reciprocity of repeated Prisoner's Dilemmas — it is trust in the face of genuine coordination risk.