game theory

Problem 4: [30 pts] Consider the problem of Dell and its production of computers. In order to sell its computers, Dell must buy an Intel chip for each computer that it sells. However, Intel is the sole supplier of these chips and so exercises market power over Dell in its supply decision. To model this scenario, we study the following dynamic game. The game begins with Intel rst setting a price p; E [0, 100]. Then after observing this price, Dell decides on a price pp 2 [0,100]. Given these prices, the demand for Dell computers by consumers is determined by: Q0030) = 100 PD- Since each computer that Dell sells must contain an Intel chip, it must purchase Qp(pp) units of chips from Intel at the chosen price of 10;. Suppose there are no further costs of production. Thus, the utility (prot) functions of the rms are: MUM; P0) = Pr(100 - PD): momma) = (PD - Pr)(100 PD)- Port a..- {10 pts/ Solve for the NE of the proper subgame after Intel decided on a price of p; G [0, 100] for its chips. Part E]: [10 pts} Solve for the subgame perfect Nash equilibria of this game. What is the chosen strategy prole? What is the actual price that Dell chooses in equilibrium? Part c: [10 pts] Suppose hypothetically that Dell and Intel decided to merge so that all Intel chips can be produced without cost to Dell. Let's call this giant monopoly Delltel. Suppose that Delltel is a monopolist with demand given by: Q = 100 p. As a result, if the monopolist chooses a price p 2 0, then it would obtain prot of: (100 - 11);?- What price would the monopolist choose? Compare this to the solution from Part 1)? Which scenario would the consumers prefer? Discuss the intuition