Credibility problems make deadlines difficult to impose. For example, imagine that your business just made an employment offer to Sue. Your company would like to hire someone quickly and would prefer that Sue accept or decline your job offer within one week. You know that Sue, however, has another job interview scheduled in two weeks. While Sue would prefer this other job, she has only a tiny chance of obtaining it. If you could force Sue to decide within one week, you’re confident she would accept your offer rather than take a chance on her long-shot dream job. Unfortunately, you messed up in the job interview and signaled to Sue that you really wanted to hire her. If you told her that she had to decide within a week, she would ignore your deadline, confident that you would grant an extension.
What if you told Sue that you
another candidate the job if Sue didn’t accept within a week? Again, since you already revealed your true inclinations, Sue would have no reason to believe this promise, because it would be in your interests to break it. What if you tried gaining credibility by giving up control of the situation? Perhaps you could go on vacation for a few weeks and instruct your human resource manager to give Sue one week and then offer the job to another candidate. This vacation strategy is flawed because Sue would never believe that you would really implement it. It would always be in your interests to tell Sue she has only a week, but then tell your HR manager to give Sue an extension if she ignored your deadline.
Should we let criminals purchase clemency? Say that a captured criminal offers to compensate his victim in return for the victim dropping all charges. If the victim agrees, should the government go along?
Actually, game theory shows that individuals can be too
. Imagine that you have just been mugged. Trauma causes mugging victims to lose far more than just their stolen property, so assume that although the mugger got $30 from you, he caused you $9,000 worth of mental anguish. Fortunately, the mugger was caught and faces one year in jail. He offers you everything he has, say, $3,000, to drop the charges. Should you accept? Why not? If the mugger
, you are extremely
to become one of his future victims. Sure, the mugger did $9,030 of damage to you, and he is offering only $3,000. If he goes to jail, however, you get nothing, so you’re better off accepting the mugger’s offer.
Unfortunately, being able to pay off victims will embolden muggers. Consequently, all decent
would probably be better off if we were
from offering muggers compensated clemency.
Consider the game
in Figure 5, where the mugger first decides whether to mug you at
. If he mugs, then nature moves at
. Nature represents the random forces of the universe that determine whether the mugger gets caught. The mugger perceives that there is a 1 percent chance that he will get caught at
. If the mugger is caught at
, then you decide at
whether to send the mugger to jail or get paid $3,000. Let’s make the likely assumption that the mugger would prefer paying $3,000 to going to jail. Thus, from the point of view of the mugger, it is more beneficial to mug you if at
you would accept the $3,000 because in the 1 percent of the time the mugger gets caught he won’t go to jail. True, if the mugger gets caught and pays you $3,000, he is
off for having mugged you. Reducing the harm to the mugger of getting caught, however, makes the mugger more likely to strike.
you are probably better off accepting the $3,000. Since you have already been harmed, sending the mugger to jail won’t erase the trauma. Of course,
you wouldn’t get mugged at
The mugger might have
only because he knew it would be in your interest at
to accept the money. Thus, you might have been better off if in the beginning of the game you could credibly promise to send the mugger to jail if the game ever reached
. In the Figure 5 game this promise not to accept the mugger’s money lacks credibility. Consequently, you would benefit from a law that forbids you to drop charges in return for a
payment from the mugger. Players often have insufficient incentives to punish those who have done them wrong.