Once I was a deer hunter ... with my photo camera
There are several types of “games” like the
Prisoner’s Dilemma. I discussed already the Prisoner’s Dilemma itself, the
Tragedy of the Commons and the Chicken Game. To finish this mini-series about
games I want to treat the Stag Hunt Game. Game theory is a rather new branch of
mathematics. It was developed during the Second World War. However, its roots
are older and the idea of the stag hunt game was already mentioned by
Jean-Jacques Rousseau (1712-1778). In his A
Discourse on Inequality he describes it this way (quoted from Bovens, p.
160; see Sources below]:
“If it was a matter of hunting a deer,
everyone well realized that he must remain faithful to his post; but if a hare
happened to pass within reach of one of them, we cannot doubt that he would
have gone off in pursuit of it without scruple ...”
A group of hunters decides to hunt deer
together, since a good way to do this is with a group: They drive the deer to a
corner of the wood, and if they see one, they shoot it. However, if one of the
drivers leaves his post, there will be a gap in the chain of drivers and the
animals will have room to escape. So if you want to hunt deer in a drive, it is
best for each hunter to cooperate and to assume that the others will do as
well. But, as Bovens says “if I cannot be assured that others will cooperate
then it is better to defect”, and so take my chance to shoot a hare that rushes
by, for maybe others will take their chances as well, if they see one, even
though cooperating would be better, provided that everybody does. Anyway, this
is so if you value a deer more than a hare and if enough deer will be shot for
all. Although cooperation is what normally should be expected, the uncertainty
what others will do (“take your chance”) plus the wavering character of many
people (“shall I abide by my decision to cooperate?”) makes that cooperation is
often so difficult.
This time I’ll leave it to you to make a
payoff matrix, but the case made me think of the fable of the fox in the hen run.
A farmer makes a net fall to catch a fox that each night steals one of his
chickens. The next night the fox is caught and the noise awakens the chickens
in the coop. “Help me”, the fox cries, “for the farmer will kill me”. The chickens
don’t want to do it, glad that the fox has been caught. However, the fox
promises “I’ll do anything you say, if you free me.” The chickens don’t trust
him, for might the fox not kill one of them, once released? Who says that he’ll
keep his promise? Then one of the hens gets an idea and says: “If we set you
free from this trap, will you remain here in this coop and protect us from any
other foxes that try to get in?” Since his life is at stake, the fox agrees and
promises to stay with them for the rest of his life. At first the chicken don’t
trust him, but after careful consideration, they decide to set him free. For will
it not also be advantageous if the fox stays with them? If the farmer kills the
fox, soon another fox will come and steal chickens and the whole story will
start anew. Maybe that fox will be smarter and will not let himself be caught.
And so it happened that the chickens freed the fox, the fox kept his promise,
and chickens and fox lived peacefully together and the latter chased away all
foxes that tried to catch one of the birds.
Maybe the case of the fox in the chicken
coop is not a pure stag hunt game, but the moral is the same: Often you are
better off to cooperate. This is so if you do, because you are in trouble and
have no choice, but also even if you know that the other cooperates because
s/he has no choice.
Postscript: These things can happen in
real:
Sources
- Bovens, Luc, “The Tragedy of the Commons
as a Voting Game”, in Martin Peterson (ed.), The Prisoner’s Dilemma. Cambridge: Cambridge University Press,
2015; pp. 156-176 (especially p. 160).
- “The Fox in the Chicken Coop”, on website http://internetstoryclub.org/fables/20_the_fox_in_the_chicken_coop.html
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