Stag Hunt Game Explained - Trust vs the Sure Thing

The setup

Two hunters split up at the treeline. Bringing down the stag needs both of them and pays 5 each. A hare is a sure 3, but chasing it abandons the stag - and a hunter left holding for the stag alone gets 0. What should each do?

Short answer: There are two stable outcomes - both hunt stag (5,5) or both take hares (3,3) - and which one you get is a question of trust, not logic.

Two equilibria, not one

If your partner hunts stag, your best reply is stag (5 beats 3). If your partner goes for a hare, your best reply is hare (3 beats 0). Each choice is a best response to itself, so (Stag, Stag) and (Hare, Hare) are both Nash equilibria.

Unlike the prisoner's dilemma, nothing dominates here. The good outcome is stable once you are in it. The problem is getting two people to believe they are both in it.

The threshold that decides it

Let p be the probability you assign to your partner holding for the stag. Stag pays 5p; the hare pays a flat 3. Stag is the better gamble exactly when 5p is at least 3 - that is, when p is at least 3/5.

That 60% line is the whole game. Stag is payoff-dominant (better for both), but hare is risk-dominant: it never pays zero. Anything that lifts confidence above the threshold - communication, reputation, a visible commitment - tips the room to the good equilibrium.

Why interviews ask it

The interview point is coordination risk: real desks face stag hunts (adopting a shared system, holding a joint position), and the follow-up is usually 'what would you change so both players choose stag?'