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Prisoners' Dilemma and its Social Implications | By Vikram Raj



Have you ever wondered why nuclear disarmament attempts always fail? Or why we have a festering problem of "free-riding" when it comes to public goods? Or on a fundamental level, why is it said that we can't live peacefully in the absence of a state formed on the basis of a social contract? This article tries to explain these phenomena by borrowing some ideas from the yet developing but fascinating branch of social sciences called Game Theory, devoted to studying strategic decisions. Ideas from the game theory have very wide applicability and can help us understand many social situations. "Prisoners' Dilemma" is one such idea which I'm going to use to explain the need for social cooperation or theoretically a "social contract".

To illustrate what this dilemma is all about, let's turn to one of its classic representations given by one of its earliest developers A. W. Tucker:

Suppose there are two prisoners A and B, suspects of a major crime, taken into custody for interrogation. They have been put in separate cells and are being questioned. Interrogating officers offer a deal to both A and B to make them confess. Here is what they say to A:

We know you have committed this crime. We can prove it and keep you in jail for 1 year. Though if you testify against B you'll be released immediately. But if B testifies against you and you keep quiet, you will go to prison for 15 years. If both testify against each other, both will face a sentence of 7 years.

The situation becomes more clear if the information is presented in the form of a "pay-off matrix" as follows:

 

What do you think the prisoners will do? Probably you may have guessed that keeping their mouths shut is the best option available for them. But think about it, if A has even the slightest belief that B is not going to confess then he will happily confess and be let off completely. Also, if A is going to consider the mutual interest and keep his mouth shut, then there is this looming fear of B's confession which will put him behind the bars for 15 years. Therefore, if A thinks rationally, for him the best bet is to confess. Because this way if B turned out to be a sucker A will be released immediately and even if B confessed, it's better for A to serve 7 years of imprisonment than 15 years. It appears that regardless of what B does, it's better for A to confess. To confess here is A's "dominant strategy". In game theory, what we call the dominant strategy is the one that is better than all other available strategies no matter what strategy the other player chooses. It's said that if you have a dominant strategy, just use it. Also, B will think no differently than A. He has the same deal, so he'll reason the same way, and he'll, too, end up confessing. So, to confess is the dominant strategy for both the prisoners. Instead of getting out in 1 year, now they will have to serve for 7 years. This is the dilemma that rational calculations lead to an action that is against the common good.

At this point, one can't help but think of the ways through which this dilemma can be overcome. Should the prisoners have signed an agreement, before they got caught, to avoid it? Should they have created the prospect of a suitable punishment to be inflicted in case of defection to deter the temptation to cheat? The answer is yes. These are some preliminary ideas for resolving the dilemma. Looking closely, you may find that the solutions mentioned here like an agreement, which everyone agrees to, and the scope of a suitable punishment in case of non-compliance constitute the basics of any social contract.

Now consider the situation of the Hobbesian man in the state of nature prior to the formation of civil society and the social contract. You'll find many parallels with the situation of prisoners of the prisoners' dilemma. First, let's look at some basic assumptions that Hobbes makes about the state of nature:

1.      Human beings have a restless desire for power. They are always in search of power. And, the search for power is, by nature, competitive.

2.      Human beings are, by nature, equal. They possess roughly the same level of strength and skill.

3.      In the state of nature there is a scarcity of goods.

What logically follows from these assumptions is that in the state of nature one must be prepared for self-preservation at any cost. Since there is a scarcity of goods and people who want to acquire those goods are equal, no one can be sure that they will not be invaded by others. If I lowered my guard on self-preservation, my neighbour will likely invade my property because, in the state of nature, attacking others is the surest way of getting what you want. But so would I, if he has lowered his guard on preserving his property. Self-preservation will drive us both to fight each other. To desist him, there is only one way for me that is to attack him first. And my neighbor too will think on parallel terms and would want to attack me first to desist me. Again here, the dominant strategy for both of us is to attack the other. Again, we will be led to an action that is against the common good. Had we had chosen cooperation we both would have been better off.

Now we can understand why Hobbes says that the rational human actions will make the state of nature a battlefield. What's the solution? How can this dilemma be overcome? The sole escape, according to Hobbes, is to abandon the state of nature and form a social contract to enforce cooperation and therefore peace. A designated sovereign should be invested with whatever powers required to preserve properties and other rights. Thus, a social contract, granting sovereign guarantee to people that their rights will be protected, is justified because it gives strong incentives to people for social cooperation required to resolve the dilemma.

Another poignant example of the prisoners' dilemma can be found in the failure to achieve nuclear disarmament. Consider two sovereign states P and Q. Both want an upper hand over each other. Sovereign states exist in an international setting that is very similar to the Hobbesian state of nature. For they don't transfer their arms and their sovereignty to an overarching authority or a super-state. Think about how peace is going to be established between these two countries. Both P and Q will have to choose between two strategies - "arming" and "disarming"- without knowing what the other is going to choose. The payoff matrix for both countries is given below:

Again, they both will end up arming themselves as both will be caught on the horns of the dilemma. For P, since it doesn't know whether Q will arm or disarm, the best option is to arm itself so that it can avoid defeat. And of course, it may even get the victory if Q turned out to be a sucker. Country Q too will reason on parallel terms as P and will opt for arming itself no matter what P does. Thus, even if the best case for both of the countries is to disarm themselves and establish costless peace, they will both go for the second-best option which is the armed peace or peace at a cost. What it tells us is that cooperation between countries to achieve costless peace is highly unlikely in the absence of an overarching authority or a super-state like structure that can enforce cooperation. This is why we need international organizations like the UN, WTO, IMF, etc.

 The essence of the prisoners' dilemma is this: a rational human being would be better off only if he acts in a purely selfish way. But if everyone acts in their own self-interest then we all will be worse off than if everyone cooperates- even if it seems irrational to cooperate. The inherent tension between the individual self-interest and the common good is what defines this dilemma.

Also, this is in contrast with what the free market economists tell us that individuals acting in their self-interest will always do better as a whole. One good example in this regard is this: suppose we live in a country where there is an acute power shortage. The government asks us to voluntarily help them in fighting the power deficit. I would reason like this: if everyone else is going to conserve power then it is better for all of us. So I should not worry about power conservation because in a country of millions a mere individual's extra consumption will not make any difference. But what if everyone is going to reason the same way. If everyone is going to think that his/her efforts are pointless in front of the population of millions, the problem will only be exacerbated. This is called the public goods problem, broadly equivalent to what is called the multi-person prisoners' dilemma. Again, the solution is to enforce cooperation that can be easily done through government intervention. Government through its coercive measures is likely to succeed in enforcing cooperation and thus, promoting the common good.

 In conclusion, I'd like to present an illuminating example of how we should think about this dilemma when caught up with it.

If you've seen the film The Dark Knight, remember its jaw-dropping climax where two ferrying boats, rigged with explosives, are leaving the city. One is carrying average civilians while the other is full of hardcore criminals of the city. Recall what conditions Joker gives them if they have to survive. He informs them that one must detonate the other before midnight or he'll blow up all of them. Here Joker assumes that people on the boats will act in their self-interest and will blow up each other. Isn't the situation here strikingly similar to that of the first example of prisoners' dilemma we saw earlier involving the two prisoners? However, as you know, Joker fails in realizing his evil intentions because on one of the boats a  prisoner takes the detonator and throws it out of the window and people on the other boat too don't find the courage to press the detonator. How did they overcome the dilemma? Batman gives the answer when he tells the joker: “This city just proved that it’s full of people ready to believe in good.” The sense of justice, morality, and the belief in the soul of Gotham was so entrenched in them that even the strongest provocation didn't deter them from following the right course of action and choosing social cooperation. Instead of acting in the pursuance of self-interest, they went for the common good rescuing everyone from the evil designs of Joker.


VIKRAM RAJ

B.A. LL.B. (Hons), 1st Year

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