Consider the market for used cars in a town in a given month. The market contains 400 potenital buyers and 400 potential sellers of used cars. Buyers and sellers are randomly matched, and within each pair, they attempt to negotiate a price at which to transact (if they fail to find a mutually agreeable price, the seller keeps the car). It is common knowledge that the sellers of second-hand cars can be of four possible types. . 44 (ie., 100) of the sellers are of type ta, attempting to sell a car that is worth $10,000 to a buyer and $8,000 to a seller. 14 of the sellers are ype tz, attempting to sell a car that is worth $7,000 to a buyer and $5,000 to a seller. 44 of the sellers are of type t2, attempting to sell a car that is worth $5,000 to a buyer and $4,000 to a seller. y of the sellers are of type t, attempting to sell a car that is worth $0 to a buyer and $0 to a seller. O (i) If the buyers can observe the seller's type, describe a Nash equilibrium of this game and calculate the resulting total surplus. (ii) If he buyers cannot observe the seller's type, describe a Bayesian Nash equilibrium of this game and calculate the resulting total surplus. (iii) Suppose sellers can pay $500 to obtain a certified mechanic's report that will reveal their type to buyers. Describe the Bayesian Nash equilibrium of this game and calculate the resulting total surplus (treating the cost of mechanics' reports as a deadweight loss). Consider the market for used cars in a town in a given month. The market contains 400 potenital buyers and 400 potential sellers of used cars. Buyers and sellers are randomly matched, and within each pair, they attempt to negotiate a price at which to transact (if they fail to find a mutually agreeable price, the seller keeps the car). It is common knowledge that the sellers of second-hand cars can be of four possible types. . 44 (ie., 100) of the sellers are of type ta, attempting to sell a car that is worth $10,000 to a buyer and $8,000 to a seller. 14 of the sellers are ype tz, attempting to sell a car that is worth $7,000 to a buyer and $5,000 to a seller. 44 of the sellers are of type t2, attempting to sell a car that is worth $5,000 to a buyer and $4,000 to a seller. y of the sellers are of type t, attempting to sell a car that is worth $0 to a buyer and $0 to a seller. O (i) If the buyers can observe the seller's type, describe a Nash equilibrium of this game and calculate the resulting total surplus. (ii) If he buyers cannot observe the seller's type, describe a Bayesian Nash equilibrium of this game and calculate the resulting total surplus. (iii) Suppose sellers can pay $500 to obtain a certified mechanic's report that will reveal their type to buyers. Describe the Bayesian Nash equilibrium of this game and calculate the resulting total surplus (treating the cost of mechanics' reports as a deadweight loss)
