Stag Hunt
The Stag Hunt is a two-player coordination game with two pure Nash equilibria: both players commit to a joint plan that pays more, or both go it alone for a smaller but safer payoff. The central question is trust, because committing pays off only if the other player commits too.
Payoff matrix
| Row player (rows) / Column player (columns) | Commit to the joint plan | Go it alone |
|---|---|---|
| Commit to the joint plan | (5, 5) Nash equilibrium | (0, 3) |
| Go it alone | (3, 0) | (2, 2) Nash equilibrium |
Payoffs are ordinal scores from the DecisionPlay engine's template for this game, 0 to 5, higher is better. They rank outcomes and are not dollar values. [MODELED]
Nash equilibria
- Pure: Row player plays Commit to the joint plan, Column player plays Commit to the joint plan. Payoffs (5, 5).
- Pure: Row player plays Go it alone, Column player plays Go it alone. Payoffs (2, 2).
- Mixed: Row player plays Commit to the joint plan 50%, Go it alone 50%; Column player plays Commit to the joint plan 50%, Go it alone 50%. Expected payoffs (2.5, 2.5).
Computed by the DecisionPlay solver from the matrix above. [MODELED]
Where it shows up
Illustrative
- Hunters and the stag. The textbook origin: hunters can cooperate to catch a stag, which feeds everyone, or each can hunt a hare alone, which is smaller but certain.
- A joint investment. Two firms can each commit to a shared venture that pays well only if both commit, or each can pursue a smaller project that does not depend on the other.
Common misreadings
- Cooperation is the equilibrium because it pays more. Both mutual commitment and mutual going-alone are equilibria. Higher payoffs do not by themselves tell players which one they will reach.
- It is just a Prisoner's Dilemma. In a Prisoner's Dilemma each player is tempted to defect from mutual cooperation. In the Stag Hunt no one gains by deviating from mutual commitment; the obstacle is assurance, not temptation.
Try it
Map your own scenario or edit a payoff matrix in the solver.