Game Theory.

Consider a Stackelberg competition game with three firms. Firm 1 chooses 1 first. Firm 2 observes 1 and chooses 2. Firm 3 observes both and chooses 3. These three firms are the only firms in the market, so the sum of their outputs is equal to total market supply, i.e. 1+2+3=. Suppose demand is given by =12. For simplicity of calculation, suppose each firm has marginal costs of 0, i.e. 1(1)=0, 2(2)=0 and 3(3)=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?