Crawl Across the Ocean

Tuesday, August 10, 2010

63. The Stag Hunt

Note: This post is the sixty-third in a series about government and commercial ethics. Click here for the full listing of the series. The first post in the series has more detail on the book 'Systems of Survival' by Jane Jacobs which inspired this series.

Just a short post this week, more of an intro to next week's post than anything else. I covered most of this ground back here, but I wanted to formally include it in the series on ethics.

We've talked a lot here about the Prisoner's Dilemma, but another type of interaction / game that comes up when talking about ethics is the 'Stag Hunt.'

Wikipedia summarizes the Stag Hunt as follows:

"In game theory, the stag hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.

The stag hunt differs from the Prisoner's Dilemma in that there are two Nash equilibria: when both players cooperate and both players defect. In the Prisoners Dilemma, however, despite the fact that both players cooperating is Pareto efficient, the only Nash equilibrium is when both players choose to defect."

Here's an example:

                              Stag                    Hare
Eve          Stag:      [2,2]                 [0,1]
                 Hare :     [1,0]                [1,1]

Unlike in the Prisoner's Dilemma where Adam's best choice would be to defect (hunt Hare) no matter what Eve does, in this case, Adam's response depends on what Eve is doing. If Eve is cooperating (hunting Stag) then it makes sense for Adam to hunt stag (cooperate as well). If Eve isn't going to cooperate, then Adam shouldn't cooperate either.

You can see how this dynamic sets up the two equilibiria that Wikipedia mentioned:

1) A 'good' equilibrium where hunters catch deer, the most valuable game animal in the forest. Because the deer is elusive, catching it requires cooperation between the hunters.

2) A 'bad' equilibrium where the hunters don't cooperate, and are not able to catch the deer so they catch rabbits instead, which can be caught without cooperation, but are not as tasty and meaty as deer. Mmm, venison.

In the 'bad' equilibrium, the hunters know they could do better by working together to catch a deer, but because nobody can act on his own (you can't catch the deer without help) and because they can't be sure that if they go to hunt deer that others will help, it is safer to just catch rabbits, rather than going off by yourself to catch the deer, having nobody help you and ending up with nothing.

The description of the Stag Hunt - where you should cooperate if the other person does and defect if they do - may also sound reminiscent of the Tit for Tat strategy that performed so well in the repeated Prisoner's Dilemma tournaments that Robert Axelrod described in 'The Evolution of Cooperation'. This isn't a coincidence - having a Prisoner's Dilemma repeat over time and having the participants switch to defection if the other player defects, transforms the payouts from A Prisoner's Dilemma into the payouts from a Stag Hunt.

Basically, what happens is that the gain a person gets from betraying the other player in the first Prisoner's Dilemma is more than offset by the losses that follow because the other player is never again willing to cooperate with you. Taking this potential future loss into consideration, it becomes in your best interest to cooperate now - if you expect the other player to cooperate.

This last part is the rub with the Stag Hunt, and you can see why it is also sometimes known as the 'Assurance Game' - if you could only assure the other player that you were going to cooperate (maybe by signing a contract, shaking hands, or by maintaining a high seller rating on ebay, etc.) then it would be in their interest to also cooperate.

In a way, the Stag Hunt is like a stepping stone on the road from the hopeless one-time Prisoner's Dilemma style interaction, to an outcome of mutually beneficial cooperation.

It's not just the possibility of the Prisoner's Dilemma repeating that can transform the interaction into a Stag Hunt, a moral principle that places merit on being 'nice' in the sense that Axelrod used it - starting off by cooperating with people, and only stopping cooperation if the other player betrays you first - could also change the payoffs in the Prisoner's Dilemma so that they resemble the Stag Hunt instead.

More on the Stag Hunt next week.

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  • There might come a day where game theory is taught to children, for now, I'm cool with them just playing games.

    By Anonymous Driving games, at 7:50 AM  

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