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?

The above question is known as the prisoner's dilemma. It is a form of game theory. It analyses the best option for a player in a game without regard for what the other player does.

The dominant strategy is the best decision for the player without considering what the other player does or without cooperation between the players. The dominant strategy for each of the prisoners is to confess because if one confesses and the other doesn't, the one that confesses goes free. If both prisoners confesses, they get 10 years each. These is a better option than not confessing and getting either 3 years or 15 years of prison sentence.

Because both players don't confess, hence they get 3 years in prison. They could have avoided the sentence by confessing.

I hope my answer helps you