Microsoft has decided to enter the market for smartphones. After months of intensive R&D (research and development) in the labs in Seattle, Microsoft is going to launch a new cell phone, "Positron Vega", which is bound to become the only serious competitor of the "I-Phone Stellar." Microsoft's critical decision is whether to enter this market, E, or not, NE. Apple is currently the leader in this market segment. Facing Microsoft's threat to enter into the same market and compete, Apple has to decide whether to advertise aggressively its product, A, to discourage Microsoft's entry, or to advertise it mildly, M, and not try to keep the potential competitor out. Suppose payoffs are as follows: If Microsoft chooses not to enter, NE, its profits are 0, whereas Apple's profits are 15 million if it advertises aggressively, A, and 20 million if it advertises mildly, M. If Microsoft enters the market, E, and Apple advertises aggressively, A, Microsoft's profits are -5 million, and Apple's profits are 5 million. If Microsoft enters the market, E, and Apple decides to advertise mildly, M, Microsoft's profits are 10 million, and Apple's profits are 10 million. Suppose the game is played simultaneously. A M E next. Microsoft NE Apple 1. Does the game have an equilibrium in dominant strategies? Explain why. 2. Find the Nash equilibria strategies (SNE, SNE) and the corresponding payoffs of this game. Suppose the game is now sequential with Microsoft choosing first its strategy and Apple 3. Draw the sequential game (the "tree") corresponding to this situation, clearly labeling the actions and payoffs for Microsoft and Apple. 4. Describe Microsoft's and Apple's actions AM, AA for the sequential game. 5. Describe Microsoft's and Apple's strategies Sar, SA for the sequential game.