A prospective buyer is interested in buying a car. The quality of the car is known to the seller but it is unknown to the buyer. From the buyer's perspective, the car for sale can be a high quality car with probability 0.6 or it can be of low quality with probability 0.4. Nature determines the quality of the car the seller owns. After observing the quality of the car, the seller decides whether to put the car up for sale, and if so, what price to set (which can be any positive real number). The buyer observes the price of the car and decides whether to buy it or not. If the seller sells the car, then her payoff is the price the buyer paid. If the seller does not sell the car, then her payoff is equal to how much the car is worth to the seller, which is $6000 if the car is of high quality, and $4000 if the car is of low quality. The value of the car to the buyer is $7000 if it is of high quality, and $5000 if it is of low quality. If the buyer buys the car, then the buyer's payoff is equal to buyer's valuation of the car, minus the price paid. If the buyer does not buy the car, then her payoff is 0. a) Does this game have a separating equilibrium in which the high quality cars are more expensive than the low quality cars? Explain your answer carefully. You have to specify the strategies of the firm, the strategies of the applicants and the beliefs of the firm when defending your argument. b) Does this game have a pooling equilibrium? Explain your answer carefully. You have to specify the strategies of the firm, the strategies of the applicants and the beliefs of the firm when defending your argument. A prospective buyer is interested in buying a car. The quality of the car is known to the seller but it is unknown to the buyer. From the buyer's perspective, the car for sale can be a high quality car with probability 0.6 or it can be of low quality with probability 0.4. Nature determines the quality of the car the seller owns. After observing the quality of the car, the seller decides whether to put the car up for sale, and if so, what price to set (which can be any positive real number). The buyer observes the price of the car and decides whether to buy it or not. If the seller sells the car, then her payoff is the price the buyer paid. If the seller does not sell the car, then her payoff is equal to how much the car is worth to the seller, which is $6000 if the car is of high quality, and $4000 if the car is of low quality. The value of the car to the buyer is $7000 if it is of high quality, and $5000 if it is of low quality. If the buyer buys the car, then the buyer's payoff is equal to buyer's valuation of the car, minus the price paid. If the buyer does not buy the car, then her payoff is 0. a) Does this game have a separating equilibrium in which the high quality cars are more expensive than the low quality cars? Explain your answer carefully. You have to specify the strategies of the firm, the strategies of the applicants and the beliefs of the firm when defending your argument. b) Does this game have a pooling equilibrium? Explain your answer carefully. You have to specify the strategies of the firm, the strategies of the applicants and the beliefs of the firm when defending your argument
