Four Hollywood actors, Al, Robert, Brad and Tom are choosing between joining or not joining a film project. They have the following preferences. Al prefers not to join if Robert is joining; otherwise, he would prefer to join. Robert prefers not to join if either Al and/or Tom join; otherwise, he prefers to join. Brad prefers not to join if Al joins; otherwise, he prefers to join. Tom prefers not to join if either Robert and/or Brad join; otherwise, he prefers to join. a. Is there a Nash equilibrium where Al and Brad both join? Why or why not?
b. Is there a Nash equilibrium where only Robert and Tom join, but the others do not? Why or why not?
c. Is there a Nash equilibrium where only Robert and Brad join, but the others do not? Why or why not?
d. Is there a Nash equilibrium where only Al and Tom join, but the others do not? Why or why not?