Prevolio
Game theoryClassroom · multi-user

Stag Hunt — Coordination & Trust

Paired for several rounds, each of you picks Stag (hunt together for the best payoff — but only if your partner joins) or Hare (a safe, fixed reward alone). See whether trust builds toward the payoff-dominant outcome or retreats to the safe one.

You’ll learn: See how the best outcome needs mutual trust rather than beating a temptation — and why players may retreat to the safe choice even when cooperating is itself an equilibrium.

Teacher guide

Students will learn to

  • Experience a coordination game where cooperating is an equilibrium — the obstacle is trust, not temptation.
  • Distinguish the payoff-dominant outcome (hunt the stag together) from the risk-dominant one (take the safe hare).
  • Watch whether repeated play builds the shared expectations needed to coordinate on the better outcome.

Before the session — ask

  • If the best reward needs your partner to commit too — but going solo is safe — which would you pick first?
  • How is this different from the Prisoner's Dilemma, where betraying your partner is tempting?

After the session — discuss

  • Did pairs drift toward hunting the stag together, or retreat to the safe hare over the rounds?
  • What made trust build (or break) between partners across rounds?
  • Where in teamwork, partnerships, or joint ventures does this same 'we both have to commit' problem show up?

Timing

  • Briefing & pairing3–5 min
  • Five coordination rounds6–10 min
  • Reveal & discussion8–10 min

Run it with your class

Students join with a code or QR — no account needed. Teachers start a session from the dashboard.

Join with a codeFor teachers

What is the stag hunt?

The stag hunt is a coordination game about trust rather than temptation. Two hunters can each go after a stag or a hare. A stag is the big prize, but it can only be caught if both hunters commit to it together; a hare is smaller but can be caught alone, guaranteed. So there are two stable outcomes — two Nash equilibria: both hunt stag, or both take the safe hare. Hunting stag together is payoff-dominant — it gives everyone the best result. But taking the hare is risk-dominant — it's the safer bet, because it doesn't depend on trusting your partner to show up. The dilemma isn't that betraying your partner is tempting (as in the prisoner's dilemma); it's that you might retreat to the safe hare out of fear the other person will. What decides the outcome is shared expectations: if each trusts the other to go for the stag, they reach the best result, but doubt can send both scurrying to safety even though mutual cooperation is itself an equilibrium. The stag hunt captures why great collective outcomes — teamwork, standards, treaties, investment — need mutual trust and confidence, not just aligned interests.

How the simulation shows it

Paired over several rounds, each of you picks Stag (the best payoff, but only if your partner joins) or Hare (a safe, fixed reward alone), and you watch whether trust builds toward the shared prize or retreats to the safe option. Playing it yourself shows the real obstacle isn't temptation but doubt about what your partner will do.

Common misconceptions

Frequently asked questions

What is the stag hunt?
A coordination game where two players each choose a risky high-reward option (stag) that pays off only if both choose it, or a safe guaranteed option (hare) they can take alone.
What are the two Nash equilibria?
Both hunt stag (the best outcome for both) and both take the hare (the safe outcome). Each is stable — given what the other does, neither wants to switch.
What is the difference between payoff dominance and risk dominance?
Payoff dominance is the equilibrium with the best result for everyone (both stag); risk dominance is the safer one that doesn't rely on trusting your partner (both hare). They can point to different choices.
How is the stag hunt different from the prisoner's dilemma?
In the prisoner's dilemma defection is tempting even if the other cooperates. In the stag hunt there's no such temptation — mutual cooperation is an equilibrium; the barrier is fear the partner won't commit.
Why do players sometimes choose the safe option?
Because of doubt about the partner. Without trust that the other will go for the stag, the guaranteed hare is the risk-dominant, safer choice — so shared expectations decide the outcome.