3. Two firms, Firm 1 and Firm 2, are competing with each other in a market with the objective of maximizing their own profit. Each firm must choose whether or not to advertise their product, which is costly but can increase the firm's sale. If neither firm advertises their profits are equal to 18 and 13 for Firm 1 and 2, respectively. If both firms advertise their profits are equal to 10 and 12 for Firm 1 and 2, respectively. If Firm 1 advertises but Firm 2 does not, then their profits are 20 for the former and 7 for the latter. If Firm 2 advertises but Firm 1 does not, then Firm 1 gets a profit of 9 and Firm 2 a profit of 17. a) Write down the strategic form of this game. b) Find the Nash equilibrium (there is only one). ) Find the cooperative outcome. Explain why this is not strategically stable. Now, suppose that instead of competing with each other only once, the two firms share the market in the way modeled above indefinitely. At the end of each period, both firms can tell what occurred in the game in that period and receive their respective payoffs. Each one discounts the future using a discount factor denoted by &, and , for Firm 1 and Firm 2, respectively. Moreover, suppose that both firms use the grim-trigger strategy of cooperating as long as the other firm has cooperated, and playing the Nash equilibrium strategy forever if it has not. d) What is the smallest value of &, that makes cooperation in every period an equilibrium choice for Firm 1? You must prove your answer. e) What is the smallest value of 0, that makes cooperation in every period an equilibrium choice for Firm 2?7 You must prove your answer. f) Explain any difference in your answer to parts d) and e)