Two competing firms must choose their quantity of production simultaneously. Each firm can either choose a Low quantity of 2 or a High quantity of 3. The price for both firms is determined by the following: P = 9 - Q1 - Q2, where Q1 is quantity of Firm 1 and Q2 is quantity of Firm 2. Costs are zero, so the profit for each firm is simply price times the quantity they produce.

a. Draw the payoff table and find the Nash equilibrium.

b. If this game were instead played sequentially, with Firm 1 choosing first, what will be the outcome of the game? Compare this to part (a). (Hint: set up extensive-form game and use backward induction.)