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3. Consider a similar entry game (with 5 companies) as in Lecture 5 (you can read the lecture slides), but now suppose that Company 1 faces zero entry cost. Company 5 faces an entry cost of $1200, and each of the other companies faces the same entry cost of $300. Each company can choose either enter or do not enter. Given the total number of companies in the market, the following table reports a company's gross profit if it enters. The payoff from entering is a company's gross profit minus its entry cost. The payoff from staying out of the market is zero. Entry Game with Identical Companies Number of Companies that Enter Gross Profit per Company 1 1000 2 400 3 350 4 150 50 5 (a) Can you tell what Company 1 or 5 do in a Nash equilibrium? Explain your answer. (10%) (b) Is there a Nash equilibrium in which 3 companies enters? If so, find all such Nash equilibria. Explain your answer. (10%) (c) Is there a Nash equilibrium in which 4 companies enters? Explain your answer. (5%) (d) Find all the Nash equilibria. Explain your answer. (10%) 3. Consider a similar entry game (with 5 companies) as in Lecture 5 (you can read the lecture slides), but now suppose that Company 1 faces zero entry cost. Company 5 faces an entry cost of $1200, and each of the other companies faces the same entry cost of $300. Each company can choose either enter or do not enter. Given the total number of companies in the market, the following table reports a company's gross profit if it enters. The payoff from entering is a company's gross profit minus its entry cost. The payoff from staying out of the market is zero. Entry Game with Identical Companies Number of Companies that Enter Gross Profit per Company 1 1000 2 400 3 350 4 150 50 5 (a) Can you tell what Company 1 or 5 do in a Nash equilibrium? Explain your answer. (10%) (b) Is there a Nash equilibrium in which 3 companies enters? If so, find all such Nash equilibria. Explain your answer. (10%) (c) Is there a Nash equilibrium in which 4 companies enters? Explain your answer. (5%) (d) Find all the Nash equilibria. Explain your answer. (10%)