Question

Bob and Tom are two criminals who have been arrested for burglary. The police put Tom and Bob in separate cells. They offer to let Bob go free if he confesses to the crime and testifies against Tom. Bob also is told that he will serve a​ 15-year sentence if he remains silent while Tom confesses. If he confesses and Tom also​ confesses, they will each serve a​ 10-year sentence.​ Separately, the police make the same offer to Tom. Assume that if Bob and Tom both remain​ silent, the police only have enough evidence to convict them of a lesser crime and they will serve​ 3-year sentences. a. Use this information to write a payoff matrix for Bob and Tom.

b. Does Bob have a dominant strategy? If so, what is it?

c. Does Tom have a dominant strategy? If so, what is it?

d. What sentences do Bob and Tom serve? How might they have avoided this outcome?

Answer 1

a)
`\left[\begin{array}{ccc}&T con&T sil\\B con&0,0&0,15\\Bsil&15,0&10,10\end{array}\right]`

b) Bob has a dominant strategy: to confess

c) Tom has a dominant strategy: to confess

d) since both will choose to confess , they will serve a 10 year sentence. They would have avoided this problem if they would have been able to talk to each other after the offer to agree on the (silent, silent) outcome.

Step-by-step explanation:

This is a popular riddle known as the prisoner's dilema.

a) the payoff matrix is

`\left[\begin{array}{ccc}&T con&T sil\\B con&0,0&0,15\\Bsil&15,0&10,10\end{array}\right]`

where in x,y : x=Bob's payoff and x=Tom's payoff

b) Bob has a dominant strategy, to confess: that is , if he confesses, no matter what tom will do ( if he confesses or not), his payoff is better than remain silent :

Strategy 1 ) Confesses → gets 10 or 0 years

Strategy 2 ) Remains silent → gets 15 or 3 years

therefore is always better strategy 1 than 2

c) the same applies to Bob , since both are indifferent and the conditions are the same

therefore also Tom will choose to confess

d) since both will choose to confess , they will serve a 10 year sentence.

They would have avoided this problem if they would have been able to talk to each other after the offer to agree on the (silent, silent) outcome.