Fergie and Abdul Were Caught by the Police in the Vicinity

Essay

Fergie and Abdul were caught by the police in the vicinity of a robbery site. The police have a strong feeling the two individuals are the actual robbers, but they do not have a way to prove it yet. In the absence of hard evidence, the prosecutor can convict them of only a minor offence, with only a year in prison. The police put the two in separate rooms and try to offer them incentives to confess: if one of the robbers does so, he would go
scot- free while the other goes to prison for 10 years. If both confess the prosecutor will be able to put both in prison for 5 years. As a result, each partner in crime has two options: to confess or to remain silent.
Note: here payoffs are in years of prison, so less is better.
a)Represent this game in normal form. Are there dominant strategies for these robbers?
b)What s the Nash equilibrium of this game?
c)How is this game called?
d)What exactly is the dilemma that the two robbers have? Is there a way to get around this problem