Question 3. Lisa is walking home late at night when suddenly she realizes that

there is someone behind her. Before she has a chance to do anything, she hears, I have a gun, so keep your mouth shut and give me your wallet. Lisa doesnt see a gun but does notice that the mugger has his hand in his coat pocket, and it looks like there may be a gun in there. If there is no gun, Lisa thinks she could give the mugger a hard push and make a run for it. But if there is a gun, there is a chance that trying to escape will result in her being shot. She would prefer to hand over her wallet than risk serious injury. Earlier that evening, the mugger was engaging in his own decision-making as he debated whether to use a gun. Because the prison sentence is longer when a crime involves a gun, hed really like to conduct the theft without it. This situation is depicted in the figure below:

a) Write each players actions and strategies. [8 marks]

b) Find all the subgames. Provide reasoning for your answer. [8 marks]

c) Find all the subgame perfect Nash Equilibria. Show all the workings and steps. [14 marks]