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 is also 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) Matrix is shown below

	Tom
Bob		Confess	Remain silent
	Confess	(-10, -10)	(0, -15)
	Remain silent	(-15, 0)	(-3, -3)

b)  Bob has a dominant strategy of confessing because its sentence is reduced to 10 instead of 15 if he confesses (in case Tom confesses) and to 0 from 3 if he confessess (in case Tom remains silent)

c) Tom has a dominant strategy of confessing because for him also, its sentence is reduced to 10 instead of 15 if he confesses (in case Bob confesses) and to 0 from 3 if he confessess (in case Bob remains silent)

d) They serve a sentnce of 10 years following their dominant strategy. Both prisoners can choose not to confess and get a lower terms for sentence but they cannot communicate so they choose a lower payoff outcome. By communicating or coordinating, they can reduce their sentence to 3 years by remaining silent.