2. Coffee Fund Part 1 [3 points] Diane is collecting money for the Center for the Study of Democratic Politics coffee fund. She needs to collect $2 from at least three faculty members to operate the fund for the month. No member can contribute more that $2 and Diane cannot exclude non-contributors from drinking coffee, so each faculty member decides whether to contribute $0 or $2. Each center member has an estimated $10 benefit from coffee service. If less than $6 is contributed, Diane keeps the money and no coffee is provided. If more than $6 is contributed, Diane provides the coffee and pockets the difference.

(a) Assume that Diane decides to ask the faculty members in the following order: Arnold, Bartels, Lewis, Prior, and Romer. Assume that each faculty member can observe who has contributed and who hasnt. What are the set of Nash equilibria to this game? [Hint] Think about what each Professors best response would be, depending on who else contributes. I dont recommend writing this part as a matrix or game tree. (b) What is the unique Nash equilibrium that survives backwards induction?

3. Coffee Fund Part 2 [3 points] Keep the same costs/benefits of contributing to the coffee fund from above, but modify the game somewhat so that Lewis, Prior, and Romer do not know whether or not Arnold and Bartels contributed. Further suppose that Lewis, Prior, and Romer must decide simultaneously.

(a) Draw this game, paying particular attention to which Professors know who else contributes, and when they know this. [Hint] You will need to draw a game tree and a matrix, but you do not have to solve for Nash equilibria in the matrix, there will be many. Instead, think about each Professors best response and information set as you draw and solve the game. (b) What are the subgame perfect Nash equilibria to this game? (c) What if Diane can choose the information structure of the game i.e. she can choose which contribution decisions are revealed at which stage. Suppose she wants to maximize the amount of money she keeps and does not care bout coffee consumption. Which game should she choose, the game from Part 1 or the game from Part 2?