The prisoner’s dilemma game is one of the most important models in all of social science: Most games of trust can be thought of as some kind of prisoner’s dilemma. Here’s the classic game:

Two men rob a bank and are quickly arrested.

The police do not have an airtight case; they have just enough evidence to put each man in prison for one year, a slap on the wrist for a serious crime.  lop85 If the police had more evidence, they could put the men away for longer. To get more evidence, they put the men in separate interrogation rooms and offer each man the same deal: If you testify against your accomplice, we will drop all the charges against you (and convict the other guy of the full penalty of 10 years of prison time). Of course, if both prisoners take the deal, the police will have enough evidence to put both prisoners away and they will each get 6 years. And, as noted above, if neither testifies, both will get just 1 year of prison time. What’s the best thing for each man to do?

In each cell in the table below, the first number is the number of years Butch will spend in prison, and the second is the number that Sundance will spend in prison given the strategies chosen by Butch and Sundance.

If years in prison are minuses, then we can write up the problem like this:

a. If Sundance keeps quiet, what’s the best choice (highest payoff) for Butch: keep quiet or testify?

b. If Sundance chooses testify, what’s the best choice for Butch: keep quiet or testify?

c. What’s the best choice for Butch? What’s the best choice for Sundance?

d. Using the definition in this chapter, does Butch have a “dominant strategy”? If so, what is it?

e. What is your prediction about what will happen?

f. How does this help explain why the police never put two suspects in the same interrogation room? (Note the similarity between this question and the earlier Adam Smith quote.)

Transcribed Image Text:

Sundance Keep quiet Testify Keep quiet (-1,-1) (-10, 0) Butch Testify (0, -10) (-6,-6)