Let us consider an industry composed by three firms x, y and z. Assume that firms have the same cost structure, that is, C(qi) = 10 + 4qi, where qi denotes firm i's output and i = {x, y, z}. In addition, the industry demand is P(Q) = 20 - Q, where Q denotes the aggregate output, where Q = qx + qy + qz. The structure of the game is the following: (i) Firm x is the first mover of the game and it chooses its output level; (ii) firm y is the second mover of this game, and after observing qx, firm y chooses its own output, qy; (iii) finally, after observing both firms output, firm z chooses its output qz. The timing of production, industry demand and cost function are common knowledge among firms. Find values of output level qx, qy, qz in the SPNE of the game