Tuesday, August 25, 2009

The prisoners' dilemma

In the classic example of the prisoners' dilemma, two suspects have been arrested. The police do not have enough evidence to convict the perpetrators of a serious crime (e.g., a felony), but are assured of conviction on a lesser charge (e.g., a misdemeanor).
The prosecutor wants to induce a confession from at least one of the suspects in order to obtain a conviction of the larger crime.
So the suspects are separated and interrogated. Each is offered the following deal:
*You must make a choice without knowing what your partner in crime has chosen.
*If you stay silent and your partner stays silent, you both will be convicted of a lesser charge and will serve 1 year in jail.
*If you stay silent, but your partner confesses to the serious crime, then you will go to jail for 20 years. Your partner in crime will go free and serve no time in jail. (A plea agreement typically results in a reduced penalty.)
*If you confess, but your partner remains silent, then your partner will go to jail for 20 years. You will go free and serve no time in jail.
*If you confess and your partner confesses, then you both will be convicted of the more serious crime. But because you both cooperate with the prosecutor, your prison sentences will be reduced. You both will serve 5 years in jail.
If you and your partner in crime are acquaintances with no loyalty to each other, what decision do you make. Do you confess or stay silent?

Remember you do not know what your partner will choose. So let us consider both possibilities. If your partner confesses, then your options are (a) to confess and serve 5 years, or (b) to stay silent and serve 20 years. Confessing seems clearly preferable. (You would prefer to spend 5 years in jail rather than 20 years.) If your partner stays silent, then your options are (a) to confess and go free, or (b) to stay silent and serve 1 year in jail. Again, confessing seems clearly preferable. (You would prefer to spend no time in jail than to be in prison for 1 year.) So regardless of your partner's decision, it seems preferable for you to confess to the more serious crime.

Your partner has the same incentive structure. So regardless of your decision, it seems preferable for your partner to confess to the more serious crime, also. Thus, the likely outcome is that you both confess and go to jail for 5 years. Yet, there was option available in which you and your partner would have been better off. If you both remained silent, each of you would serve significantly less jail time.

So this is the prisoners' dilemma: Choosing what seems to be in your self interest may not be. Selfishness may not lead to optimal solutions, for society as a whole or you as an individual. You and your partner would be better off if you make choices than seem to go against your self interest.

So how can we arrive at the optimal outcome?

Suppose the two suspects have genuine love for each other, rather than being just acquaintances. (For example, suppose the two criminals are Bonnie Parker & Clyde Barrow.) Suppose you would be willing to serve a longer prison sentence if it allowed your partner to serve less time. If both partners feel this way, then you both might choose to remain silent. The outcome is then the optimal one.

Humanitarians and religious leaders urge people to show more love and compassion to one another. (Love your neighbor ... and everyone is your neighbor.) So a cultural revolution in which love and compassion become prominent might lead to more optimal social outcomes. In the absence of that, however, there may be yet another rationale for government intervention in the marketplace. (Indeed, if people demonstrated more love and compassion to each other, there would be less need for government.)

For example, the primary justification for large taxes on alcohol and tobacco is to increase the price of them to discourage their consumption. The government intervenes in the markets for these products because society deems it beneficial. The free market frequently provides outcomes that are socially undesirable. Unregulated markets create too much pollution, poverty, and market power. And free markets create too little national defense, public health, education, roads, and other public goods. Thus, despite the proclamations of many free market advocates, most people agree it is appropriate and indeed necessary for the government sometimes to intervene in the marketplace.

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