Plea bargaining and the prisoner's dilemma
The prisoner's dilemma has been widely cited as an illustration of how individual incentives and external effects can lead to socially undesirable outcomes. But this is a very narrow view of the prisoner's dilemma. Under certain circumstances, prisoner-dilemma-like situations can also lead to efficient outcomes and be a source of welfare efficiency. Indeed, the original story from which the prisoner's dilemma derives its name is one of success and an efficient outcome for the prosecutor - not the failure and the socially undesirable outcome that is emphasised so often.
To see this, suppose that there are two criminals who have committed a crime and have been charged by the prosecutor. The prisoners both know that they are guilty of the crime, as does the prosecutor. However, the goal of the prosecutor is to have them confess to the crime, so that a costly trial is avoided. The prosecutor's problem is to design a mechanism or incentive scheme in which it is in both criminals' individual self-interests to confess, and that they voluntarily do so - even though they would both be better off if they did not confess.
This is a simple problem in mechanism design, which has a very simple solution. Suppose that the prosecutor announces a menu of fines. First, if both prisoners confess, the fine is f_{cc}. Second, if one prisoner confesses and the other does not, then the fines are f_{cd} and f_{dc} respectively, where f_{dc} > f_{c}. Finally, if both fail to confess, they will each face a fine of f_{dd}, where f_{dd} > f_{d}. In addition, it is assumed that the prisoners' most preferable outcome is for them to both not confess, so we further assume that f_{dd} > f_{cc}. The payoff matrix of this game is shown in Table 9.4.1.
Table 9.4.1 The payoff matrix for the prisoner's dilemma
Prisoner 2 |
|||
Confess |
Don't Confess |
||
Prisoner 1 |
Confess |
(fcc, - fee ) |
(-fed, - fde ) |
Don't Confess |
(, - fed ) |
(-fdd,^{- f}dd) |
As is well known, the dominant strategy equilibrium in this situation is for both prisoners to confess, and the outcome is that they both face a higher fine than they would have if they had both not confessed. That is certainly a bad outcome for the prisoners. But from a broader social welfare perspective, this is exactly the outcome that the prosecutor desires. Both prisoners confess and an unnecessary, costly trial is avoided. In this broader sense, the equilibrium of the prisoner's dilemma leads to an efficient outcome.