[Play Smarter with Game Theory] Level 3: Stag Hunt - Why the Safe Option Isn’t Always the Smart One

Play Smarter with Game Theory
Level 3: Stag Hunt - Why the Safe Option Isn’t Always the Smart One

Two hunters in a forest can either work together to hunt a stag, which will feed them both for days, or they can each hunt rabbits alone. Rabbits are easy to catch but a stag is worth more. A stag can only be caught if both hunters commit. If one decides at the last minute to chase a rabbit instead, the other goes home empty-handed.

This is the Stag Hunt, a classic game theory scenario about cooperation. Here’s the payoff matrix:

(The numbers are example payoffs, the higher the better)

A Nash equilibrium is a situation where no player can increase their payoff by changing their choice if the other player keeps theirs the same. In other words, once you’re in that spot, nobody has an incentive to move.

In this setup, there are two Nash equilibria:

• Both hunt stag (4, 4)

• Both hunt rabbits (2, 2)

That “empty-handed” outcome is why many people settle for rabbits. Choosing rabbits means less reward, but avoids the worst case. Once players settle into an equilibrium, they tend to stay there. The Stag Hunt is about whether you can trust the other player enough to take the bigger risk together.

We can see the Stag Hunt in business when two companies consider a joint venture, in everyday life when classmates decide whether to start a project together, and even in global issues like combatting climate change. Countries could all benefit if everyone commits to cutting emissions (the stag), but if some back out, those who invested more will risk economic loss while others take the “rabbit” path of doing less. The payoff from mutual commitment is greater, but so is the disappointment if only one side cooperates.

The Stag Hunt shows us that some of life’s best rewards only come when everyone commits. Whether it’s a business deal, a group project, or a global climate agreement, trust turns risk into opportunity. Without it, we’ll keep settling for rabbits.

Next time we’ll explore Mixed Strategies and why adding a bit of unpredictability to your moves can make you much harder to beat.