Find the SPE of the game.

Question
There are two firms in an industry. In period 1, Firm 1 has to decide how much to invest in advertising a ≥ 0. In period 2, after observing a, both firms decide simultaneously their prices p1 and p2. The profits of each firm depends on the actions of the other, in particular, profits are given by π2 = 90 + 2p1p2 − p12 − p2 − 2a2 and π1 = 80 + p1(a − p1) + p1p2 − a3/3. Find the SPE of the game.

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