A hare in the hand, or a stag in the bush
In 1755, Jean-Jacques Rousseau described early humans hunting together. A deer could feed everyone, but only if every hunter held their position. Any one of them could also catch a hare alone.
If a deer was to be taken, every one saw that, in order to succeed, he must abide faithfully by his post: but if a hare happened to come within the reach of any one of them, it is not to be doubted that he pursued it without scruple.Rousseau, Discourse on the Origin of Inequality · trans. G. D. H. Cole
That small scene turns out to describe a huge range of situations: teams, markets, alliances, friendships, and early-stage investing. It's now one of the core models in game theory. Below, we'll build it from nothing and prove what it tells us, step by step. No background needed.
Strip it down to what's true
Every strategic situation has four parts: who is choosing, what they can choose, what they get for each combination of choices, and what they know. For the stag hunt, that's six plain facts:
- Two hunters, A and B.
- Each chooses one thing: hunt the stag or hunt a hare.
- They choose at the same time, with no way to see the other's choice first.
- A stag is caught only if both hunt it. Then they share it.
- A hare can be caught alone, for sure, whatever the other does.
- Each hunter simply wants the most food for themselves.
That's it. Everything that follows is derived from these six sentences.
The payoff board
Let's give each outcome a value. Half a stag is worth S = 4. A hare is worth H = 3. Hunting the stag while your partner wanders off gets you L = 0. The exact numbers don't matter. What makes it a stag hunt is the order:
Lay every combination out on a two-by-two board. Each square shows what A gets, then what B gets.
Your numbers carry over to the charts in the next chapters.
Your best move depends on theirs
Put yourself in A's place and ask: if I knew what B was doing, what should I do?
| If B hunts… | A hunting stag gets | A hunting hare gets | A's best response |
|---|---|---|---|
| Stag | S = 4 | H = 3 | Hunt the stag |
| Hare | L = 0 | H = 3 | Hunt the hare |
Neither choice is better in every case. Since S > H, stag is better when your partner hunts stag. Since H > L, hare is better when your partner hunts hare. QED
So the right move depends entirely on what you expect the other person to do. Hold on to that sentence; it's the whole game. (The same table holds for B, because the game is symmetric.)