Two firms, F1 and F2 face the market price given by p = a q1 q2. Both firms produce output with no fixed cost nor marginal cost. The cost of advertisement is given by a 3 100 where a [0,) is the level of advertisement. The pay-offs are given by (a q1 q2)q1 a 3 100 for 2P1 and (a q1 q2)q2 for P2. In period 1, F1 selects the level of advertisement a. In period 2, F2 observes F1's period 1 choice a and selects its level of output q2 [0,). In period 3, F1 observes F2's period 2 choice q2 and selects its level of output q1 [0,). (1) Find the SPE. (2). Find a Nash eq. that is different from the SPE found in (1), and explain why it is Nash eq. but not a SPE.