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 for whoever chases it, but chasing it abandons the stag, and a hunter left waiting for the stag alone gets 0. What should each hunter do?
Short answer: There are two stable outcomes, both hunt stag (5, 5) or both chase hares (3, 3), and hunting the stag is right only if you believe your partner will hold with probability at least 3/5.
Step 1: Find every best response
If your partner hunts the stag, your options are 5 (stag) and 3 (hare), so stag is your best reply. If your partner chases a hare, your options are 0 (stag) and 3 (hare), so hare is your best reply. Each action is the best reply to itself.
That makes both stag-stag and hare-hare Nash equilibria. Unlike the prisoner's dilemma, nothing dominates here. The good outcome is stable once both players are in it; the problem is getting there.
Step 2: Turn trust into a number
Let p be the probability you assign to your partner holding for the stag. Hunting the stag pays 5 with probability p and 0 otherwise, so its expected value is 5p. Chasing the hare pays a flat 3 whatever your partner does.
Stag is the better bet exactly when 5p is at least 3, which is when p is at least 3/5. That 60% line is the whole game. Below it, the rational hunter takes the hare even though both would prefer the stag.
Step 3: Payoff dominance versus risk dominance
Stag-stag is payoff dominant: it is better for both players than the other equilibrium. Hare-hare is risk dominant: it never pays zero, and it is the better choice when you are maximally unsure, at p = 1/2, because 3 beats 2.5.
Experiments show that groups often drift to the safe equilibrium, especially when the stakes of being stranded are high. Anything that lifts the shared belief above 60% tips the room to the stag: communication, a track record, or a visible commitment that is costly to reverse.
The threshold moves with the payoffs. If the stag paid 10 each, you would need only p ≥ 3/10. If the hare paid 4, you would need p ≥ 4/5. Being able to recompute it on the spot is the skill the interviewer is testing.
Step 4: Where it shows up in trading
Two desks agreeing to adopt a shared risk system, two market makers both tightening their quotes, a team committing to a joint position: each is a stag hunt. The value is only there if everyone holds, and the risk of holding alone is what keeps people on the hare.
Why interviewers ask it
The strong answer computes the 3/5 threshold, names the two kinds of dominance, and then answers the obvious follow-up: what would you change so both players choose stag?
Knowing the proof is half of it. Work Stag Hunt interactively, then take it under a clock with the rest of the Outcry simulators.