THE STAG HUNT

Two equilibria. One requires trust. One does not.

Player 2
Cooperate Defect
Player 1 Cooperate Stag, Stag 3 , 3 Nothing, Hare 0 , 2
Defect Hare, Nothing 2 , 0 Hare, Hare 2 , 2
Trust Basin
payoff-dominant 		Safe Hare Basin
risk-dominant

Stag is the best reply when the partner hunts Stag with probability above 2/3. For the symmetric replicator law p′ = p(1 − p)(3p − 2), starts below 2/3 approach Hare and starts above it approach Stag. A uniform initial p gives attraction fractions 2/3 and 1/3 in this model. Safe defection is not coercion.

Payoffs plus a specified replicator model

Replicator potential SAFE HARE wider attraction interval under uniform initial p ridge at p = 2/3 TRUST (STAG) pays more smaller attraction interval 0 2/3 1 share of hunters choosing Stag (p) → potential V Replicator potential SAFE HARE wider attraction interval ridge, p = 2/3 TRUST (STAG) pays more, narrower 0 2/3 1 share choosing Stag (p) →
p = 0.50
Stag3 × p = 1.50 Hare2, guaranteed

Both pure strategies are Nash equilibria. Under the chosen replicator law, both endpoints attract and p = 2/3 is unstable. The potential is illustrative dynamic geometry, not thermodynamic energy. No stochastic escape claim follows.

core conceptemergent / positiveconstraint / breakdown