Results of Prisoner's Dilemma exercise from class
In class you and a partner were accused of a criminal activity, but the evidence was thin. You were put into separate rooms so that you couldn't confer with each other, and told the following:
If you deny the charges and your partner also denies the charges, you will get 5 hours of community service.
If you confess and give us evidence against your partner, while your partner continues to deny the charges (you help us get a conviction), you'll only get 2 hours of community service.
If, however, you don't admit to the charges and your partner turns you in, you will be expelled.
Finally, if you confess and your partner confesses, we'll give you 10 hours of community service.
You have two possible actions, which basically boil down to keeping quiet or confessing. Your partner has the same set up, which makes a pay-off matrix (what happens to you under different scenarios) that looks like this:
|You keep quiet||You confess|
|Your partner keeps quiet||5 hours of community service||2 hours of community service|
|Your partner confesses||Expelled||10 hours of community service|
You are in separate rooms and can't communicate with your partner in crime, so you can't affect what he or she does.
What is the best thing for you to do?
Sometimes the optimal decision will depend on what the other person does. In this case, however, note three things:
1) No matter what your partner does, you get a gain from confessing. Confessing is therefore the dominant strategy.
2) Your partner had exactly the same incentives, so the equilibrium under this set-up is for both of you to confess.
3) This is the equilibrium even though you both would be better off if you would both keep quiet.
This model is called the prisoner's dilemma, and economists use this game theory set-up to describe and predict what will happen in oligopolies. If you substitute in pay-offs that are profits, collusion for the keep quiet option, defect for the confession option, and have a set-up where the dominant strategy is to defect, you get a prediction about whether oligopolies will be able to sustain collusion or not. In equilibrium, they shouldn't.
|Pair||Trial 1||Trial 2||Trial 3||Trial 4||Trial 5|
|1||Both confessed||Both confessed||Both confessed||Both confessed||Both confessed|
|2||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet|
|3||Both kept quiet||Both kept quiet||Both confessed||Both kept quiet||Both confessed|
|4||A: kept quiet
|Both kept quiet||Both confessed||Both confessed||Both kept quiet|
|5||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet|
|6||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet|
|7||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet||Both kept quiet|
Which pairs fit the model perfectly? Only #1
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