Consider the game in the previous exercise. Suppose the players have reached a point where it is Fred’s move and there are just five matchsticks left. (a) Draw the game tree for the game starting with...

Consider the game in the previous exercise. Suppose the players have reached a point where it is Fred’s move and there are just five matchsticks left.

(a) Draw the game tree for the game starting with five matchsticks.

(b) Find the rollback equilibria for this game starting with five matchsticks.

(c) Would you say this five-matchstick game has a first-mover advantage or a second-mover advantage?

(d) Explain why you found more than one rollback equilibrium. How is your answer related to the optimal strategies you found in part (c) of the previous exercise?