Stag or Hare

How it works

Two hunters separate at the treeline and cannot signal. The stag needs both of them and pays 5 each; a hare is a sure 3 for one hunter alone, but chasing it abandons the stag - and a hunter left holding for the stag alone gets 0. The story shows the payoff matrix and asks whether there is one right answer the way there was for the prisoners. You lock in a guess, then step through the answer and breakdown.

How scoring works

No grading - your guess is displayed back beside the answer. The story teasers share one lifetime unlock for free users.

The key insight

Nothing dominates here: stag is your best reply if your partner hunts stag, hare is your best reply if they defect. That gives two Nash equilibria - (Stag, Stag) at 5 each and (Hare, Hare) at 3 each. The first is payoff-dominant, the second risk-dominant, and which one happens is decided by beliefs about the other player: stag is the better gamble exactly when you put at least a 3/5 probability on your partner holding.

The full step-by-step solution lives at /brain-teasers/stag-hunt/solution.

A worked example

Let p be your probability that your partner holds for the stag. Stag pays 5p in expectation; the hare pays a flat 3. 5p >= 3 when p >= 3/5, so above 60% confidence you hunt stag, below it you take the hare - the whole game reduces to that threshold.

Common mistakes

• Treating this as the prisoner's dilemma and declaring defection dominant - here nothing dominates.

• Naming only one equilibrium. The answer is that there are two, plus a reason for which you would expect.

• Forgetting that communication changes the answer - the entire value of talk here is moving both players to the good equilibrium.

Why interviews test this

The interview point is coordination risk and the payoff-dominant versus risk-dominant distinction. The written solution at /brain-teasers/stag-hunt/solution derives the 3/5 threshold.