PRISONERS’ DILEMMA

Pervasiveness of norms
Game theory and the Prisoners’ Dilemma
Rationality and the Prisoners’ Dilemma
Norms, the Prisoners’ Dilemma, and the free-rider                    Return to contents

Pervasiveness of norms

    Norms are often thought to have a moral standing partly because they are needed in society, and without a moral standing they would be ineffective. Evidence of this occurs in neighborhoods and institutions when ordinarily accepted norms of proper behavior begin to break down. Laws are not effective in guaranteeing smooth social functioning partly because the police cannot be everywhere. Instead, it is essential that people adopt ways of behaving, including conventional behavior, to ensure a healthy environment. Unless people accept basic social norms -- including, for example, norms about property -- social life becomes difficult.
    We have little trouble realizing that norms are needed to ensure safety and security. But theorists examining norms argue that they pervade social life. Norms establish job expectations, required educational experience, basic social communication (like how far we stand from people we engage in conversation), how we drive an automobile, whether we talk in the theater, and so on. The argument is that we need many norms to coordinate behavior; norms help us to form expectations about how other people will behave, and this allows us to adjust our behavior. Furthermore, without norms, rational people, each independently doing the "right" thing or the rational act, produce irrational results -- that is, results that deprive each of some good. Genuinely beneficial results are sometimes only secure when norms regulate behavior, so that behavior can be adequately coordinated. The proof of this comes from an example from the mathematically oriented study of "games," or formalized sequences of human actions.  Top

Game theory and the Prisoners’ Dilemma

    In game theory, the Prisoners' Dilemma shows that two people, each acting "rationally," can produce irrational results. The setting for the dilemma is a police interrogation. Two prisoners are taken and interrogated separately. The police offer each the same deal, in terms of prison time, to get them to confess, and each knows that the same offer has been made to the other. Both prisoners are assumed to be individually rational in the sense that they want the most for themselves, without thought about social norms or moral obligations. As we will see, the dilemma underscores the need for such norms.
    In game theory, to be individually rational means basically that an individual does what most benefits him or her. The dilemma is set up using simple numbers to reflect individual interests;these numbers may be varied to include special concerns, fears, and the like. In the Prisoners' Dilemma, individuals are assumed to want to avoid a jail sentence. So the numbers represent the number of years that each prisoner will be sentenced to depending on whether the prisoners confess or refuse to confess. So getting more jail time is worse than getting less. We assume that each prisoner only has two choices: confess or do not confess. These two options are represented by a matrix containing four boxes. The prisoners are called ‘A’ and ‘B’. The top two boxes of the matrix represent outcomes when A confesses. Likewise, the two left-hand boxes represent outcomes when B confesses. Thus, the upper-left-hand box represents the outcome when both prisoners confess, while the upper-right box represents the outcome when A confesses and B does not.

Prisoners' Dilemma
 

Confess

Don't Confess

Confess

          (7,7)

(2,10)

Don't Confess

(10,2)

(4,4)

    The outcomes are listed within the boxes. The upper-left-hand box shows what happens when each prisoner confesses: each gets a seven-year sentence. The first number in each box represents the sentence of A, and the second number the sentence of B. So if A does not confess and B does, then A gets ten years in prison, and B gets two years.
    The rational thing to do is confess. This is the case because no matter what the other does, each prisoner is better off by confessing. We will work this out for A, showing that no matter what B does, A is better off by confessing. Afterward, you should work this out for B, showing that no matter what A does, B is better off by confessing. Keep in mind that in this simple example, being better off simply means serving less time in jail.
    B can either confess or not confess. Suppose that B confesses. A should confess as well, because by confessing, A can serve three years less jail time. If B confesses, A gets seven years by confessing, but ten years by not confessing. So if B confesses, A should confess as well.
    Suppose B does not confess, what should A do? Once again, by confessing A gets a better deal. If A confesses, A gets two years in jail, but by not confessing, A gets four years. So if B does not confess, A should confess in order to get less time.   No matter what B does, confess or not confess, A gets less time by confessing.
    As you can tell, the same analysis works to show that B should confess. If A and B are both rational, then they both should confess. Of course, the prosecutor sets up the game this way, attempting to get a confession from each.   Top

Rationality and the Prisoners’ Dilemma

    According to the received view of rationality (as pure individual interest), both should confess. If the players are rational this will be the outcome. But check out the box representing what happens when both confess: each gets seven years. Now suppose the prisoners are not rational. They act foolishly, or perhaps they act from an "irrational" sense of loyalty, and both do not confess. Each selects the irrational action. Now examine the box where neither confesses. Both get four years. In this example, if both do the irrational thing, they each come out better! Here's the dilemma: rational action produces a worse result for both prisoners than irrational action.
    In reflecting on the dilemma, we should be willing to generalize. The dilemma is presented under particular and unusual circumstances, but many more common situations are like the Prisoners' Dilemma in form. For example, it might be rational for me as an individual to walk across the lawn, violating a rule set up to prevent the establishment of an ugly dirt path. Even though I would rather walk around than see this path, I understand that my own action, as an individual, has little bearing on the formation of a path. So I save the time and walk on the lawn, understanding that if others do the same, a path will form regardless of my actions, and if others do not, I won't have a noticeable effect on the lawn. No matter what others do, I am better off taking the shortcut. If all of us act irrationally, no path is formed, but if we all act rationally, a path occurs, which we all would have preferred to avoid.  Top

Norms, the Prisoners’ Dilemma, and the free-rider

    The Prisoners' Dilemma is a dramatic way to show that uncoordinated individual action can lead to less than optimal results. Solving the problem by an appeal to norms will not help unless those norms effectively serve as constraints on individual action. This is seen in the problem of the free-rider, a person who takes advantage of the fact that others behave properly, which is also involved in the example of the lawn. Suppose not confessing is held as a norm. A knows that B is an honorable person, but A refuses to be guided by norms. A confesses, while B follows the norm and does not confess. In this way A gains from the norm without following it. A is a free-rider because A does not pay the price involved in conforming to the norm, yet A reaps the benefits involved in having a norm. The result: A gets two years while B gets ten. This is certainly not a desirable outcome for B.
    Norms need to be supported by the social power that typically keeps people from acting against them. Perhaps this power is backed by moral education, by social sanction, or by the manipulation of general institutional arrangements. The last way occurs when an institution is organized such that people generally gain by being moral or by following moral norms and lose by being immoral. The institution thereby carries much of the burden of supporting moral behavior.
    One way to enforce solutions to Prisoners' Dilemma problems is through laws, but we know that unless laws are internalized, at least to some degree, enforcement lags behind violations. Norms help to secure the effectiveness of the law; norms, including moral norms, do get taught and do get internalized. They provide a way to solve problems suggested by the Prisoners' Dilemma.   Top

See also:

     AGREEMENT IN MORAL THEORY: DAVID GAUTHIER
     NORMS: THEIR MORAL STATUS
     NORMS AND THE THEORY OF GAMES