Prisoner’s Dilemma!

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What is common to Climate Change and Controlling Pollution? If I add over exploitation of our oceans and uncontrolled use of plastics into the mix, you can no longer claim that they begin with “c” but you might claim that they are all “wicked” problems. Let me throw in the use of skin brightening creams related to colorism into the mix. Most people will claim that this is not a wicked problem, although those caught up in the fairer skin competition across large parts of the world will disagree. The simple answer is a game called Prisoner’s Dilemma! The story underlying Prisoner’s Dilemma as economists will tell you is as follows.

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Two members of a criminal gang have been arrested and are being questioned by the police in separate cells and cannot communicate with each other. They are suspected of a major crime. Here are the possible outcomes: If neither of them confesses, the cops can pin a small crime on them which will put them each in prison for 2 years. If both confess, they will get a 10-year sentence each. Ideally, they should both just keep mum and get the smallest sentence possible, i.e., the 2-year sentence. But here comes the complication If one of them confesses, that person will become State witness and get 0 years in prison, while the other person will get 20 years in prison. This little deal being offered by the police changes everything. 

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Following the standard assumptions in game theory we will assume that each prisoner is rational and is only interested in their own payoff. Moreover, this information is common knowledge − an assumption that is just as vital as the ceteris paribus part when stating the Law of Demand. We say something is common knowledge when we all know that we all know that we all know… ad infinitum. Let us now examine how each prisoner will reason in this game: suppose the other prisoner is going to confess, what should I do? I should confess, otherwise he will be a State witness and I will get the 20-year sentence. Suppose the other prisoner is not going to confess, what should I do? I should confess because then I get to be a state witness and get no prison time. So no matter what the other prisoner does, I should confess! Now in this clever little scenario set up by the cops both prisoners will end up confessing and going to prison for 10 years each.

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This little story has even made its way into movies, most famously in the movie Murder by Numbers. Two homicide detectives have put two young boys they suspect of murder in two separate rooms and are questioning them. As Ryan Gosling’s character Richard, who is the driving force behind the murder keeps stalling, one of the detectives quite tells him that the other boy Justin, is being questioned in a separate room and he is talking! Going back to our wicked problems, suppose tackling climate change requires restricting certain types of economic activities and investment in costly technology. Then every country would like other countries to do this to address climate change, while they themselves prefer not to be shackled by these efforts. Unfortunately, every country thinks like this, and we are unable to tackle Climate Change.

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The same thing happened with nuclear weapons during the Cold War. If the Soviet Union was going to build a nuclear stockpile, then so should the United States. If the Soviet was not building a nuclear stockpile, then it was better for the United States to build a stockpile and be the only superpower. Unfortunately, both countries reasoned the same way and ended up with a large stock of nuclear weapons using resources that could have been put to better use elsewhere. The key insight from Prisoner’s Dilemma is that in many instances there is a conflict between what is good for society and what is good for the individual and selfish behavior takes us to the bad outcome which is the only stable outcome (aka Nash Equilibrium) of the game.

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How does this relate to colourism? Everyone would be better off not using skin brightening creams. However, if the others are using it (and you have been brainwashed by the fair skin brigade), then you have to use it. More importantly, if the others are not using it then you will feel the need to use them. In fact, you can extend the argument to the entire cosmetics industry which has managed to persuade us that their products will make us feel better and/or help us get ahead.

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Prisoner’s Dilemma has a fascinating history. Shortly after the publication of Von Neumann and Morgenstern’s book: Theory of Games and Economic Behavior in 1944, World War II ended, and the Cold war began. At that time, the RAND Corporation, which was a think tank set up by the US Air Force to analyze conflicts and offer superior strategies wholeheartedly embraced game theory. Two scientists at RAND – Melvin Dresher and Merrill Flood came up with the outcomes captured by Prisoners Dilemma. The story of the two prisoners to describe the game however is attributed to Princeton mathematician A.W. Tucker (of Kuhn Tucker fame) who was also John Nash’s advisor. Apparently, when he was visiting Stanford, Tucker’s office was near the sociologists who kept poking fun at the esoteric nature of his work. The story of the two prisoners that has now become the mainstay of all game theory courses was his responses to the sociologists. He wanted to demonstrate how a large number of human interactions can be covered by a simple game, a truth that continues to hold even today.