Game Theory · GT-12
Two equilibria, one much better than the other — and getting there requires trusting your partner won't bail.
A coordination game with two pure Nash equilibria: both players hunt stag together (high payoff, but only works if both commit), or both hunt hare alone (low but safe payoff, achievable regardless of the other's choice). Unlike the Prisoner's Dilemma, mutual cooperation here is stable once reached — the challenge is trust, not incentive to betray.
Rousseau described the underlying scenario in his 1755 Discourse on Inequality; the formal game-theoretic name and matrix analysis came later, in 20th-century game theory literature.
The Mechanism
The trust threshold — which equilibrium you land on depends on confidence, not incentive
Both (Stag,Stag) and (Hare,Hare) are genuine Nash equilibria — neither player wants to deviate unilaterally from either. The entire game turns on which one gets selected, and that depends on trust and shared expectation, not on incentive to cheat.
01 · NOT A PRISONER'S DILEMMA
Cooperation is stable here, unlike PD
Once both players are hunting stag, neither has any incentive to defect to hare — (Stag,Stag) is a genuine equilibrium, not a trap waiting to unravel. This is the critical difference from the Prisoner's Dilemma: the problem in Stag Hunt isn't temptation to betray, it's uncertainty about whether the other side will show up.
02 · RISK-DOMINANCE vs. PAYOFF-DOMINANCE
Two competing rules for which equilibrium to expect
(Stag,Stag) is 'payoff-dominant' — strictly better for both. (Hare,Hare) is 'risk-dominant' — safer if you're at all unsure what your partner will do, since hunting hare guarantees you something regardless. Game theorists (notably Harsanyi and Selten, 1988) have long debated which criterion better predicts real behavior — and evidence suggests both operate depending on context and communication.
03 · COMMUNICATION AND TRUST-BUILDING ARE NOT INCIDENTAL — THEY'RE THE MECHANISM
Unlike PD, talking actually helps here
Because both equilibria are stable once reached, credible communication, reputation, and trust-building genuinely shift which equilibrium gets selected — this is why Stag Hunt is the canonical model economists use for analyzing how institutions, culture, and communication enable large-scale cooperation that pure incentive analysis alone can't explain.
Where It Fails / Inversion
Where it fails / inversion
Treating every coordination failure as a Stag Hunt (fixable purely through more trust and reassurance) misses situations that are actually Prisoner's Dilemmas in disguise — where a party's incentive is to defect regardless of what the other does, no amount of trust-building changes the underlying temptation, and coordination without an actual incentive fix is fragile.
How To Use It
Worked example · startup co-founder equity commitment
Two co-founders can build a much more valuable company together (the stag) than either building alone (the hare) — but each risks wasted years if the other bails early. The real barrier isn't that either founder wants to betray the other for personal gain; it's uncertainty about commitment. Vesting schedules, public announcements, and early visible investment of resources function as trust-building signals that shift both parties toward committing to the higher-payoff equilibrium.
How to use it
When a group is stuck in a safe-but-mediocre equilibrium despite a better one being available to everyone, ask whether the barrier is genuine incentive to defect (a Prisoner's Dilemma — fix the incentives) or simply uncertainty about whether others will commit (a Stag Hunt — fix it with credible signals, sequencing, and visible early commitment).
See Also