The Stag Hunt mosaic from Pella (
by Craig Stellmacher
May 1, 2013, 2:00 PM

Stag Hunt and Guns

Almost 20 years ago now, I was out running hills one day in Wirth Park, blasting headphones on a warm sunny day… When I ran by four teenage boys. I said “hello” as I ran by them, and then they shot me.

It felt like someone had hit my shoulder with a baseball bat. I looked up to see if a tree fell on me, and then I looked back to see them laughing at me and aiming again.

I ran away in a zig zag pattern so as not to get shot, and then I doubled back a mile to the park office and we called police. I was taken to Hennepin County Medical Center.

“I can see it; I can feel it,” as the doctor fished in my shoulder for the bullet. But an x-ray would show it went right through me. Afterwards, I was too scared to run in private places, and would only run the lakes of Minneapolis for safety…

 – o O o –

With time and perspective, I can now analyze this in a different way, rationally with Game Theory.

Let’s play Stag Hunt!

You will find it in Jean Jacques Rousseau’s “Discourse on Inequality” about four books before the birth of liberalism’s book: “The Social Contract.”

There are 9 Nobels for Game Theory in Economics, that start about 1940 with John Von Neumann’s “MiniMax Theorem.” When ever you hear “Game Theory,” make it easy on yourself and substitute the words “Strategy Theory” instead, please; they were statisticians who thought it up, and they thought of all problems as gambling problems, hence “Game Theory.”

Only, a few centuries earlier, Rousseau came up with this one, Stag Hunt.

Look–in the clearing is a huge stag–and his antlers are so big he can not leave the clearing easily. The trees are so dense all around…

But, there are 20 paths that lead off, too…

Wait, let’s count how many we have with us: 16, 17, 18, 19, 20! If we each hold an opening, we can capture this stag, worth 20 points, together!

Only thing is, just now by you, ran a bunny worth 5 points. You do the math, and you opt out after the bunny… “I only get 1 point, if I share with all of you; I get 5 if I opt out for the bunny!”

What do we get then?

Nothing: the Stag leaves down your unprotected path.

– o O o –

Please note: for Rousseau the Stag represented anything, an idea. Something that had to be done TOGETHER.

You may wish to ponder this model this way: Democrats tend to want to stand in a circle and accomplish something together, Republicans tend to opt out, and say: “We all have an equal chance to capture the bunny!”

But what if you had to do something together?

The Rand Corporation wanted to model Nuclear Disarmament this way. (The Rand Corporation, named for: Research ANd Development, was set up after WWII to model Nuclear War Decisions using Game Theory. When decisions get tough, use Game Theory.)

The Rand Gamers thought: If we all worked together to disarm, we’d all be safe! Only thing is, you all kept opting out for 5 megaton bunnies. (And it is safe to assume this behavior will continue in the future.)

The same thing goes for local gun control. If we all disarmed, we’d all be safer; no one at all would get shot.

“Yes, but what if someone else at work or the beer tent has a gun?!” “I opt out, I want to be safe!”

“Why should we fight Climate Change–when the Chinese aren’t?!”

When one opts out, what do the others get?


Sadly, Stag Hunt has a natural break down point too, where you can expand out the circle till you meet “Dunbar’s Number”: the number of people you identify with as friends. You’ll share your food and shelter with them: “But the rest of you will have to get your own!”

Dunbar’s Number is seen as an artifact of evolution, mankind grew up in a village; we grew up in a village of 150. (At that point, we were nearly all 1st and 2nd cousins, and we identified and shared our food and shelter with each other.)

This number is a line plotted by Robin Dunbar, Evolutionary Anthropologist using brain size to social group size among the primates, and it is rather linear. The larger the primate brain–the larger the social group.

The average number of friends on facebook, happens to be 150! (Though the internet and facebook seem to be making it trend upwards–GOOD!)

You’ll share your food and shelter with them–but the rest of you will have to get your own!

It’s hard to convince everyone to join a Stag Hunt then to fight Global Warming, or Gun Control, when you feel there are so many outside the circle… That threaten you.

So you humans, you tend to opt out, and go get a 5 megaton bunny, or a Glock of your own.

When if we all joined a circle, we’d all be safer. If we all made our maximum payout move though, the “Nash Equilibrium,” we’d all stay in the circle. (More on the Nash equilibrium later.)

But, humans, are not rational; they are instinctual.

For the longest time, mankind has favored competition over cooperation. But that was when there were fewer of us, and now we touch elbows. Cooperators–Democrats want the circle, Competitors–Republicans want to opt out. Sometimes it pays to stay, sometimes opt out. Mathematically, in this instance, the Nash Equilibrium is to stay…

But humans don’t care; they tend to be selfish and compete.

Good news though–if humans are alive one million years from now–they will be much more cooperative.


Do you need a gun to play Stag Hunt?

The rational answer is “no;” the instinctual answer is “yes.”

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