Brain Teasers · Stag or Hare
Stag Hunt Puzzle - Trust vs the Sure Thing
The stag hunt as a story: two equilibria, and a choice that comes down to trust.
What is the stag hunt?
The stag hunt is a coordination game that traces back to a parable in Jean-Jacques Rousseau's 1755 Discourse on Inequality: a group of hunters can cooperate to bring down a stag, which feeds everyone well, or any individual hunter can break off to catch a hare alone, which is a smaller but guaranteed meal. Catching the stag requires everyone to hold their position; if even one hunter defects to chase a hare, the stag escapes and whoever stayed on the stag gets nothing.
Formalised as a two-player game, it has two pure-strategy Nash equilibria: both players hunt stag, which pays the most to each, and both players hunt hare, which pays less but is safe. Unlike the prisoner's dilemma, neither action dominates the other - hunting stag is your best response only if you expect your partner to hunt stag too, and hunting hare is your best response if you don't.
This is what makes the stag hunt a model of trust. The mutual-stag outcome is what game theorists call payoff-dominant - the better outcome for everyone if it's reached - while the mutual-hare outcome is risk-dominant - the safer choice when you're unsure what your partner will do, because it doesn't punish you for guessing wrong. Which equilibrium a group lands on depends on beliefs about the other player.
Economists and political scientists use the stag hunt to model exactly this kind of trust problem in the real world: social contracts, technology standards that only pay off if enough people adopt them, and any cooperative arrangement that only beats the safe fallback if you can be confident enough people will hold up their end. Communication or a track record of reliability moves a group toward the stag equilibrium by raising that confidence.
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.
Play Stag or Hare on Outcry
Stag or Hare is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play Stag or Hare and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.