Two hunters can bag a STAG together — a feast — but only if BOTH commit; if one peels off for a rabbit, the stag escapes and the loyal hunter goes hungry. So there are two stable outcomes: the great one that needs trust, and the safe one that needs none. Every alliance, standard, and treaty lives here. Slide your trust that the other will hold the line.
The Stag Hunt (Rousseau) is a coordination game with two pure Nash equilibria: STAG–STAG pays (4,4) and is PAYOFF-DOMINANT, HARE–HARE pays (3,3) and is RISK-DOMINANT (safe: a hare needs no partner). Hunting stag risks 0 if your partner defects to the hare, so your best move depends on your TRUST p that they’ll cooperate: hunt stag iff 4p > 3, i.e. p > 0.75. Unlike the Prisoner’s Dilemma, cooperation IS an equilibrium here — the problem is assurance, not temptation. A fail-loud self-check throws unless both stag-stag and hare-hare are equilibria and stag-stag Pareto-dominates. ◆ real game theory, node-verified.
Standard stag-hunt payoffs (the exact two-equilibria, payoff- vs risk-dominant structure and the p>0.75 trust threshold); real coordination adds communication and repeated play that build the trust — the assurance-problem core is exact.