Stag Hunt

A coordination game where mutual cooperation on the risky action maximizes welfare.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Payoffs $\begin{pmatrix}(a,a)&(b,c)\\(c,b)&(d,d)\end{pmatrix}$ with $a>c\ge d>b$ ; pure equilibria are $(S,S)$ and $(H,H)$ .

With $(a,b,c,d)=(5,0,4,3)$ , stag hunting yields $5$ if both cooperate; hare hunting gives $3$ safely.

Intuition

Everyone gains more by hunting the stag together, but hunting hare alone is safer.

Tension between payoff-dominance (stag) and risk-dominance (hare).

Worked example

A team project where collective effort yields $5$ each, individual effort $3$ , and being the lone cooperator $0$ .

International environmental agreements where only joint effort protects a common resource.

The math

Harsanyi-Selten: $(S,S)$ is payoff-dominant, $(H,H)$ is risk-dominant. Experimentally, risk-dominance often prevails.

Infinitely repeated play can select $(S,S)$ under sufficient patience.

Where it is used

The European Union's common currency is a Stag Hunt: all member states benefit from a stable euro (hunting the stag), but during crises, individual countries are tempted to pursue independent monetary policies (hunting the hare), risking currency union collapse.

Rousseau's original parable of cooperation.

Go deeper

GuideProgressive Loading: BOW to MLP to Transformer in 3 Stages

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