Stag hunt
The stag hunt is a cooperation game with no dominant strategy and two Nash equilibria. One equilibrium is much better for both players than the other, but reaching it requires trust — each player must believe the other will cooperate.
Payoff Matrix
| P2: Hunt Stag | P2: Hunt Hare | |
|---|---|---|
| P1: Hunt Stag | II | III |
| P1: Hunt Hare | I | IV |
- P1 prefers: II > IV = I > III
- P2 prefers: II > III = IV > I
There are two Nash equilibrium strategies:
- Box II — both hunt stag. The best outcome for both players.
- Box IV — both hunt hare. Safe but suboptimal for both players.
The central question of the stag hunt is: how do players coordinate on the better equilibrium?
A focal point is one NE box that has some conspicuous, prominent, or salient feature that each player can reasonably believe the other player would notice — increasing both players’ propensity to choose it. In the Stag Hunt, box II is the focal point because it is unambiguously better for both players.
Because switching from IV to II is good for both players if they move together, focal-point reasoning works relatively well here. If both players recognize that II is the obvious choice, each has reason to believe the other will choose it — which makes choosing it rational.
The assurance game looks structurally similar to a stag hunt but is harder to escape. In a stag hunt, defecting when the other player cooperates (box I or III) is no better than mutual defection (box IV). In the assurance game, defecting on a cooperating player is actually better than mutual defection — which makes the risk of switching to cooperation higher and focal-point reasoning less reliable.