Friday, 4 January 2013

Prisoners dilemma or stag hunt



Over Christmas I had chance to read The Stag Hunt and the Evolution of Social Structure by Brian Skyrms. A nice read, very interesting and thought provoking. There’s a couple of things in the book that prompt further discussion. The one I want to focus on in this post is the distinction between the stag hunt game and the prisoners dilemma game.
   To be sure what we are talking about, here is a specific version of both type of game. Adam and Eve independently need to decide whether to cooperate or defect. The payoff matrix details their payoff for any combination of choices, where the first number is the payoff of Adam and the second number the payoff of Eve. For example, in the Prisoners Dilemma, if Adam cooperates and Eve defects then Adam gets 65 and Eve gets 165.

Prisoners Dilemma

Eve

Cooperate
Defect
Adam
Cooperate
140, 140
65, 165

Defect
165, 65
90, 90

Stag Hunt

Eve


Cooperate
Defect
Adam
Cooperate
140, 140
10, 70

Defect
70, 10
70, 70

The key thing about the prisoners dilemma is that cooperating is a dominated strategy. It doesn’t matter what Eve does, it is in Adam’s interest to defect. Similarly, it doesn’t matter what Adam does, it is in Eve’s interest to defect. So, we have a clear game theoretic prediction that both Adam and Eve should defect. Simple enough. This result, however, is a bit depressing given that both Adam and Eve would get much higher payoffs if they were to cooperate. It’s this trade-off between individual rationality and collective rationality that has resulted in the prisoners dilemma, despite its seeming simplicity, being easily the most analyzed game in game theory. The key questions asked are: (i) whether people cooperate in the prisoners dilemma, (ii) if they do (many do) then why, and (iii) if they do not (many do not) then how can we get them to cooperate.
   The main thing I liked about Skyrms’ book is his suggestion that we should focus a little less on the prisoners dilemma and a little more on the stag hunt game. There are, at least, two reasons to focus more on the stag hunt game. The reason emphasized by Skyrms is that this game is often a better description of the applied context we’re interested in than the prisoners dilemma. A more subtle reason, not explicitly mentioned by Skyrms but a theme throughout the book nonetheless, is that an understanding of the stag hunt game can possibly tell us more about the prisoners dilemma than an analysis of the prisoners dilemma can do. So, what’s different about the stag hunt game?
   In this game cooperate is not a dominated strategy. If Eve cooperates then it is in Adam’s interest to also cooperate. Which suggests that it should be a lot easier to get cooperation? That, however, is where things get interesting. If you ask people to play the stag hunt game then the outcome is remarkably similar to what you get if you ask people to play the prisoners dilemma. This is the case in the two player versions given above, or in the more general many player versions (which correspond to a linear public good game and minimum effort game) where defection quickly becomes the norm. This empirical finding potentially tells us a lot. The standard story is that people defect in the prisoners dilemma because that is the rational thing to do. That story, however, sounds a little suspect if people defect to a similar extent in the stag hunt game. In the stag hunt game defection cannot be explained as the ‘rational thing to do’ and is almost certainly a consequence of people avoiding a risky option. Something similar may be going on in the prisoners dilemma. If so, it would be a mistake to put a lack of cooperation in the prisoners dilemma down to defection being the rational thing to do.
   I’m not saying that different things may not be happening in the prisoners dilemma and the stag hunt game. Clearly, the problems of obtaining cooperation in the prisoners dilemma appear greater than in the stag hunt game. My point is more of a ‘let’s walk before we can run’ nature. It seems ambitious to try and get people to cooperate in the prisoners dilemma when we don’t know how to get them to cooperate in the stag hunt game (and we don’t). My hope would be that ways of obtaining cooperation in the stag hunt game would work pretty well for the prisoners dilemma as well. And to get cooperation in the stag hunt game the emphasis must surely be on making people more confident that the person they are playing with will cooperate. This line of reasoning is quite different to that found in most of the research on the prisoners dilemma. But, it still leaves open the question of how to get cooperation in the stag hunt game. Skyrms had a lot to say on that question, which gives me a nice topic for a future post.

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