April and Ben are working on a group project. April is going to work on her part, part A, and Ben is going to work on his part, part B. April and Ben each choose whether to put in H igh effort or Low effort. Each players' payoff is a sum of two things: the final grade on the project (which is the same for both of them) and their personal cost for the amount of effort they chose.

Grade: If they both put forth High effort, their grade is 100. If only one puts forth High effort, their grade is 80. If neither puts forth High effort, their grade is 30.

Cost: If April puts forth High effort, her cost is 30. If Ben puts forth High effort, his cost is 40. Low effort has a cost of 0 for both players.

(a) (5 points) Suppose April and Ben choose their effort levels at the same time. Write the matrix form and extensive form of this game. How many subgames does it have?

(b) (10 points) Consider the game in part (a). Find all Subgame Perfect Nash Equilibria of this game and explain why they are SPNE and why you think you have found all of them. Is it possible that they earn a grade of 100? Explain.

(c) (5 points) Now suppose April chooses her effort level first and shows it to Ben, and then Ben chooses his effort level. Write the matrix form and extensive form of this game. How many subgames does it have?

(d) (10 points) Consider the game in part (c). Find all Subgame Perfect Nash Equilibria of this game and explain why they are SPNE and why you think you have found all of them. Is it possible that they earn a grade of 100? Explain.

(e) (5 points) Suppose April finishes first and has the choice whether or not to show her effort level to Ben before he chooses. Should she? Why or why not? Answer carefully.