The Farmer's Dilemma
reasonableapproximation.net
reasonableapproximation.net
I've often encountered thought experiments like this with a moral along the lines of "Some times it pays to be bad, it's upsetting, but it's the truth and here's the maths that proves it" but it's always been equally interpretable as "look how bad a job naive game theory does at explaining real life".
The interesting developments start appearing toward the end of a finite set of iterations. How long do you keep cooperating? Who defects first?
Very few people would outright say "I'm going to defect here, you'll do the work anyway". They might say "that sounds like a great idea, but I promised my kids we'd go to Disneyland this weekend". And next week, "I promised my wife some alone time". Then, "my herd is coming down with something, I need to pick up some antibiotics". And so on, until you give up and dig it yourself.
And if you install a pump in a village and ask people to pay to use it without enforcing that, they might say "I'm not going to pay, water should be free".
It would be naive to try to model everything as a simple one-shot game. It would also be naive to think that simple one-shot games don't usefully model real life at all. Just look at https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#Real-life... and see how many players defect.
However, I agree that I should probably have included some discussion of iterated versions.
Game theorists always seem to assume that there's no such thing as nuanced communication.
No, they don't. Non-iterated, binary-strategy-choice games are the simplest things in game theory, but not the whole of game theory. The same as the simplifying assumptions used at the beginning of an Econ 101 class aren't the whole of economic models.
Nuanced interactions in iterated games (and what kind of games nuanced interactions actually make any difference in) is, in fact, studied in quite some depth in game theory.
Specifically, public goods are goods where there is a temptation to free ride. As illustrated in the article, this doesn't always mean 0 public goods get made even by perfectly rational actors -- sometimes it's worth it for someone to do it anyway (Imagine putting up a street light in front of your shop if your local government didn't do it for you.)
The Wikipedia page has dozens of possible solutions, both economic and social -- everything from government provision to buying out possible free riders to subsidies to social sanctions.
"Tell you what. Go halfsies on this ditch thing with me and I'll bring over a half a pig to throw in your freezer in October."
You reduce your workload by half and you only give up 1.1 utilon. You get 1.9 utilons for 1 (1.9x efficiency) vs getting 3 for 2, which is only 1.5x efficiency.
If you have plenty of good work lined up, that's the better way to go. You'd only dig it yourself if you had a lot of free time.
Plus if you offer them something you produce yourself, you can get half of it back as profits. I.e. the foreign aid approach.
Both lost.
Maybe it's that you're about contemplating incentive structures underlying the creation of a public good rather than the traditional Tragedy of the Commons maintenance of a public good?
Rather than run the ditch between the properties, he could run it down the far side of his own, or the center, for that matter.
Wrong. By failing to dig the ditch, rainwater will now flood your properties, ruining both cars.
:)
And this is why money is nice. Because it enables the outcome with greatest total utility in this case: that the healthy guy digs the ditch by himself and gets a promise of future reward.
Curiously enough, the subject of a great many of the earliest legal codices.
> Formally, there are two Nash equilibria, at C/D and at D/C. This distinguishes it from the prisoner's dilemma, which has an equilibrium at D/D.
Giving the strategy of the actor whose payoff is considered first and the other actors second, the order of payoffs for FD is:
D/C => C/C => C/D => D/D
The payoffs for PD are:
D/C => C/C => D/D => C/D
PD has a dominant strategy of defection because independent of the other player's strategy, you always get a better result by defecting.
FD lacks a dominant strategy because whether a particular strategy improves your expected payoff depends on the other player's strategy.