3. [40\%] Three oligopolists operate in a market with inverse demand of P(Y)=aY, where Y=y1+y2+y3 and y1 is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, and no fixed cost. The firms choose their quantities as follows: (1) firm 1 chooses y10; (2) firms 2 and 3 observe y1 and then simultaneously choose y2 and y3, respectively. (a) Using backward induction (10%) and (b) find the subgame-perfect equilibrium (SPE) outcome ( 20%). (c) check the necessary, sufficient and stability conditions (10\%) 3. [40\%] Three oligopolists operate in a market with inverse demand of P(Y)=aY, where Y=y1+y2+y3 and y1 is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, and no fixed cost. The firms choose their quantities as follows: (1) firm 1 chooses y10; (2) firms 2 and 3 observe y1 and then simultaneously choose y2 and y3, respectively. (a) Using backward induction (10%) and (b) find the subgame-perfect equilibrium (SPE) outcome ( 20%). (c) check the necessary, sufficient and stability conditions (10\%)