3. Consider the following variant of the Bertrand Model: Two firms simultaneously choose prices and sell on the market. Each firm can choose ANY non-negative price and consumers buy from the firm with the lowest price. If both firms choose the same price then they each get half of the market. The demand function is given by: Q(p) = 400 - p and each firm has a constant marginal cost of producing the good c = 100. a. Find all pure strategy Nash Equilibria of this game (HINT: You need to show that the action profile you propose is a Nash Equilibrium and all other action profiles cannot be a Nash Equilibrium) (5 pts) b. Suppose that a third firm enters this market and this firm has the same marginal cost (c = 100) as the other two firms. Show that the action profile (100, 100, 101) is a Nash Equilibrium (5 pts) c. Given your answer in part (b), find all pure strategy Nash Equilibria of this game with three firms (5 pts)