In the market for search engines, Google and Microsoft produce over 82% of the services. Let's consider a duopoly for these two companies (an oligopoly with two firms). Suppose that each firm has two possible strategies: "Scale Up" or "Stay". If both companies scale up, then they will earn profits of $1 billion each. If they both stay, they will earn profits of $2 billion each. If only one company scales up, the company that scales up will earn $5 billion and the other will lose $1 billion. a. Illustrate this duopoly problem in a payoff matrix. b. Find each firm's best responses. Does either firm have a dominant strategy? c. Does this game have a Nash Equilibrium? What strategies are used by each business in the Nash Equilibrium?