(Captain's log): Petersen writes:
I've been a reader of your blog for a little while now, you have an interesting brain ;) Anyway, I've been thinking about the Tragedy of the Commons and I'd like to hear your opinion. It seems to me that the solution, where the commons would be destroyed, isn't accurate. Let me explain the game in my own terms to make the argument easier.
So you have a village that shares a commons. There are 10 villagers and the commons can support 40 sheep. Adding a sheep to the commons gets a villager +1 point, but costs him -1/10 of a point (the penalty is shared among the other villagers). The standard understanding of this game is that it's in the best interest of each villager to add as many sheep as possible to maximize their score, and if everyone does this the commons will be destroyed.
I don't buy it.
Let's say all of the villagers have 4 sheep in the commons and adding one more sheep will destroy it. At that point, the penalty would no longer be -1/10 of a point. The penalty would be enough to reduce a villager's score to 0, since the commons is destroyed and none of your sheep can eat. It seems to me that the Nash Equilibrium is for each player to use the commons to it's capacity, but not over.
The standard understanding of the game assumes that the villagers are idiots (a very European idea). But in the US, we believe that the common people can make the right choice if informed of the rules. In this model, it seems that the villagers would not destroy the commons if informed of the new penalties as the game progresses (which is one reason why radical ecologists are a good thing for this country).
Of course, the real world is a much different beast. But this model is quoted quite a bit and I just don't agree with how it's understood the game will end.
The term "tragedy of the commons" comes from reference to the case of a common grazing area, and that is usually the example which is used, but the actual term refers to an extremely broad category of phenomena which cover far more ground than that.
It's part of the exploration of the Prisoner's Dilemma; in a sense, it's a collective version of the Prisoner's Dilemma. The reason economists began to explore it was that the Prisoner's Dilemma and related things seemed to represent a case where collective decision making broke down. When individuals made decisions to optimize their own results, the overall system was seriously suboptimal. That ran opposite to the fundamental assumption behind Adam Smith's "invisible hand", where the assumption was that the overall system would be optimized when every player in the game worked to optimize their own results. (Understand that more often than not, that actually does create something like an optimal overall result. But what this exploration showed was that such optimization didn't happen invariably, and they wanted to understand the cases where it failed.)
Your objection makes an incorrect assumption about the actual analysis even when referring to a common grazing area. For one thing, there's no stairstep where N works and N+1 leads to instant and total destruction.
Rather, what happens is that at N the situation is stable and sustainable, and at N+1 there's a slow degradation over a long period. At N+1 no grazing animals starve this year, but next year the commons is only capable of supporting N-1 animals at sustainable grazing levels.
But even so, N+1 animals could still graze on it without any of them starving that year. But in so doing they cause even more degradation, and the total resource declines still further. If the overutilization level is more or less constant, then destruction accelerates because constant use at level N+1 represents progressively greater overutilization as sustainable capacity declines.
There would come a time, eventually, when animals would actually begin to starve but it is a long way into the future. (And oddly enough, in some cases there's actually more of an incentive to overutilize as the commons declines, making the decline even more rapid.)
The critical problem with your analysis is that there's actually no short term penalty for cheating at all, not even a tenth of a point. There's no disincentive, no negative feedback. Overgrazing doesn't cause your animals, or anyone else's animals, to starve this year. Therefore it doesn't reduce anyone's score, at least immediately.
On the contrary, since no animals starve in the short term, the cheater's score goes up. He grazes more animals, and they all prosper. Non-cheaters thus get a score of 4, and cheaters get a score of 5 (or 6 or 7) and win, short term.
The problem is further complicated by the fact that in most cases the value of "N", the maximum sustainable yield, isn't easily determined, especially when it's variable and influenced by stochastic processes. If the rains are good this year, the grazing area may grow particularly well. If the rain fails, it's a different matter. And humans may not even understand all the factors which are involved, because some of the systems involved are chaotic, so they may think they're operating at a sustainable rate but actually be overutilizing the resource.
Any penalties resulting from overutilization are deferred, sometimes by decades, and those who are overutilizing may not even realize they are doing so. But even when