Prisoner’s Dilemma games and the environment

Several days ago I commented on this post by my friend Novita Listyani from Bali. In my comment I promised an explanation of what I designated as the “bad game” that has trapped the customs of Balinese bird-trappers and prevents them from simply listening to the heart of a nature lover like Novita and free the birds they have trapped. This is the promised explanation, coming a little late because of some adventures with a stomach virus that you don’t need to read details about.

I will start with a story that features at the very beginning of a very good graduate microeconomics textbook by Samuel Bowles, Microeconomics: Behavior, Institutions, and Evolution. The story is this, in the words of Bowles:

“..Like the overnight train that left me in an empty field some distance from the settlement, the process of economic development has for the most part bypassed the two hundred or so families that make up the village of Palanpur. They have remained poor, even by Indian standards: less than a third of the adults are literate, and most have endured the loss of a child to malnutrition or to illnesses that are long forgotten in other parts of the world. But for the occasional wristwatch, bicycle, or irrigation pump, Palanpur appears to be a timeless backwater, untouched by India’s cutting edge software industry and booming agricultural regions.

Seeking to understand why, I approached a sharecropper and his three daughters weeding a small plot. The conversation eventually turned to the fact that Palanpur farmers sow their winter crops several weeks after the date at which yields would be maximized. The farmers do not doubt that earlier planting would give them larger harvests, but no one the farmer explained, is willing to be the first to plant, as the seeds on any lone plot would be quickly eaten by birds. I asked if a large group of farmers, perhaps relatives, had ever agreed to sow earlier, all planting on the same day to minimize losses. “If we knew how to do that,” he said, looking up from his hoe at me, “we would not be poor.””

The crux of the problem is that these farmers are trapped playing a prisoner’s dilemma. The first description of this kind of game was given in 1950, early in the days of the formal development of game theory. The game was first described via a story of two prisoners who were arrested and interrogated separately for a particular crime. The prosecutor can bring a lesser charge against each prisoner without obtaining more evidence from their confessions, but if the prosecutor can get one of them to confess to the main crime he thinks they have committed, then he can get a conviction for this more serious crime.

To induce each prisoner to confess, the prosecutor tells each, separately, that if they confess and the other does not, then the one confessing will get a more lenient sentence. For the sake of argument, suppose that the details are as follows.

  • If prisoner A does not confess and prisoner B does not confess, each gets a year in prison.
  • If prisoner A confesses and prisoner B does not confess, A gets to go free, while B gets three years in prison.
  • If prisoner B confesses and prisoner A does not confess, B gets to go free, while A gets three years in prison.
  • If both confess, each gets two years in prison.

Now put yourself in the shoes of any prisoner — the game is symmetric, so let’s imagine you are prisoner A, and everything we say will apply just as well to prisoner B. You try to decide whether to confess or not. There are two possible choices that prisoner B may make: confess, or not confess.

Suppose B is going to confess. Then if you confess, you get two years in prison, and if you do not confess, you get three years in prison. If you think B will confess, clearly it pays to confess also.

Suppose B is going to not confess. Then if you confess, you get to go free, and if you do not confess, you get a year in prison. If you think B will not confess, again it clearly pays to confess.

That prosecutor has set up the situation in a devilishly clever way! The two prisoners would be together better off not confessing, but each one has an obvious incentive to confess no matter what s/he expects the other prisoner to do.

So what, you might say. I started talking about bird trappers in Bali, and now I am muttering about prisoners. What gives? And what on earth does the story of the poor farmers in Palanpur have to do with any of this?

It all has to do with the “invisible hand” and its failure. Adam Smith, the grandpa of modern economics, made a famous analogy to an invisible hand that guides the independent decisions of people participating in competitive markets to result in a socially optimal outcome, despite the selfish motivations of these people. In Adam Smith’s own words,

As every individual, therefore, endeavours as much as he can both to employ his capital in the support of domestic industry, and so to direct that industry that its produce may be of the greatest value; every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. (Adam Smith, 1776, An Inquiry into the Nature and Causes of The Wealth of Nations, par. IV.2.9) Source

The general overconfidence of conservatively-minded politicians on markets is attributed to this statement and subsequent mathematical proofs of it, all relying on individuals participating in competitive markets. The prisoner’s dilemma game is a thorn in the side of such believers in market magic. In the prisoner’s dilemma, the players are not in a competitive market (one with many buyers and sellers) and their actions directly affect each other. Their incentives are set up so that the tantalizingly possible mutually best outcome (each in prison only for one year) is unattainable when each makes the decision to confess or not independently of the other (and there is no market price to coordinate these decisions).

A little thought will now reveal to you why I told you the Palanpur story. Think of each farmer as a prisoner. Confessing is equivalent to planting too late. Not confessing is equivalent to planting early. You can see that all farmers would be better off planting early, on the same day. But each has a strong incentive to delay, no matter what the other farmers do. So the farmers stay poor, even if a better way is available to them, if only they could somehow tie their decisions to each other’s!

Back to the bird trappers of Bali: they are also playing a version of the prisoner’s dilemma game. (This dismaying game is in fact very prevalent in real-life interactions, and you can find it at the bottom of many such interactions if you keep your eyes peeled for it.) Each bird trapper may well want to release the birds that he has trapped. But then he expects other trappers to trap them! So, why bother?

The prisoner’s dilemma game is a staple of the discussion of environmental issues since at least Russell Hardin’s famous “Tragedy of the Commons” paper. It’s worth mentioning, however, that Elinor Ostrom, the one and only (so far) female winner of the Bank of Sweden Prize in Honor of Alfred Nobel for Economics (in 2009) built her career by finding and analyzing ways that various societies have developed to evade the tragedy of the commons. I am lecturing on Ostrom’s work in my graduate class on mechanism design these days, and I want to say very much more about it, but it will have to wait for the next post on this blog, as this post is pushing up against 1,500 words already. Meanwhile, here is Ostrom’s Nobel Prize speech.

One thought on “Prisoner’s Dilemma games and the environment

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s