Game Theory. Consider a Stackelberg competition game with three firms. Firm 1 chooses q1 first. Firm 2 observes q1 and chooses q2. Firm 3 observes both and chooses q3. These three firms are the only...

Extracted text: Game Theory. Consider a Stackelberg competition game with three firms. Firm 1 chooses q1 first. Firm 2 observes q1 and chooses q2. Firm 3 observes both and chooses q3. These three firms are the only firms in the market, so the sum of their outputs is equal to total market supply, i.e. q1+q2+q3=Q. Suppose demand is given by P=12-Q. For simplicity of calculation, suppose each firm has marginal costs of 0, i.e. c1(q1)=0, c2(q2)=0 and c3(q3)=0. (1) What quantity does Firm 1 produce in the SPNE of the game? (2) What quantity does Firm 2 produce in the SPNE of the game? (3) What quantity does Firm 3 produce in the SPNE of the game?