Use the following information to solve the problems.

Pfizer has learned from corrupt bureaucrats of the coming COVID-19 pandemic, allowing the firm to choose the timing of its vaccine production decision. First, Pfizer will decide how to enter (aggressively, passively, or cooperatively). Then, the two firms will choose production levels as follows: 1. Enter aggressively (A): If Pfizer enters aggressively, Pfizer will be able to choose its production level q1 before Moderna chooses its production level q2. 2. Enter passively (P): If Pfizer enters passively, then both Pfizer and Moderna will choose their production levels q1 and 92 simultaneously. 3. Enter cooperatively (C): If Pfizer enters cooperatively, Pfizer will produce half of the production level that maximizes the two firms' total profit. After observing Pfizer's production level, Moderna will choose its production level 92 (without restriction). The inverse market demand curve is P(Q) = 1000 - 7.5Q, where Q = q1 + 92. Pfizer and Moderna both have marginal cost of 100. Pfizer's entry cost is 2000 if it enters aggressively, 1000 if it enters passively, and 500 if it enters cooperatively. Moderna's entry cost is 1000 in all scenarios. (a) Find a pure-strategy subgame perfect Nash equilibrium (SPNE). Please bold your final SPNE so that it is clear what your final answer is. (b) What is the smallest grant (i.e., subsidy) that the government needs to give Pfizer so that it will enter cooperatively? If you recommend that Pfizer enters cooperatively in (a), then please enter 0