Stag Hunts: fascinating and useful game theory model for collective action problems

Yesterday, I wrote about some Johns Hopkins students who overcame a game theory problem and got an A for the whole class. I called it a non-iterated Prisoner's Dilemma, but as Tim Harford points out, it's more of a Stag Hunt, a game theory category that I hadn't been aware of, and which has fascinating implications for lots of domains, including Internet peering:

In the stag hunt, two hunters must each decide whether to hunt the stag together or hunt rabbits alone. Half a stag is better than a brace of rabbits, but the stag will only be brought down with a combined effort. Rabbits, on the other hand, can be hunted by an individual without any trouble.
There are two rational outcomes to the stag hunt: either both hunters hunt the stag as a team, or each hunts rabbits by himself. Each would prefer to co-operate in hunting the stag, but if the other player’s motives or actions are uncertain, the rabbit hunt is a risk-free alternative.

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(Image: [ C ] Lucas Cranach - Stag Hunt of the Elector John Frederick, a Creative Commons Attribution (2.0) image from centralasian's photostream)

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http://profile.yahoo.com/SSRCITDSVSZXGIRZVOQWPOUJWE John

Obligatory alumnus correction: JohnS Hopkins.
http://www.bryanbruns.com bryanb

So, in a stag hunt, all can win, get their best outcome, if they can coordinate. Typically that depends on trust, but having everyone on guard outside the classroom is a practical way to ensure that everyone is following the cooperative strategy.

In a stag hunt there is a stable win-win Nash Equilibrium where no one has an incentive to defect. That contrasts with Prisoner’s Dilemma, where cooperation gets only second-best, and is unstable, since the individual incentive is to defect to get the best outcome (but if both defect, then both end up at second-worst.

For an interesting synthesis of research on stag hunts and their implications, see Brian Skyrms, The Stag Hunt and the Evolution of Social Structure.

There is actually a family (or herd) of stag hunts, also known as coordination or assurance games, all with two Nash Equilibria, one of which is win-win where both get their best outcome, but variations in how the other payoffs are distributed. Robinson and Goforth’s topology of 2×2 games provides a way to map how these are related by swaps in payoffs. For some enhanced visualizations of the topology (that I’ve developed), see 2x2chart.com
Philbert

Can someone explain the relevance to Internet peering?
Paul Harrison

Yes! I’ve also heard this called a “coordination game”, and it requires a strangely recursive form of knowlege called “common knowledge”, knowledge that you know everyone knows, know everyone knows everyone knows, etc. Many of the stranger things people do in groups make sense when viewed as establishing common knowledge in order to win coordination games.

See the book “Rational Ritual: Culture, Coordination, and Common Knowledge” by Michael Suk-Young Chwe.

http://www.chwe.net/michael/papers.html