Consider the game in the previous exercise. Suppose the players have reached a point where it is…

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.

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(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?

 

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