A particular model of used car comes in four categories: perfect, good, bad, and hopeless. There...

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A particular model of used car comes in four categories: perfect, good, bad, and hopeless. There are equal numbers of cars in each category. The market consists of at least two potential buyers and sellers of the car. Assume that there are equal numbers of buyers and sellers. All agents are interested in maximizing the expected surplus they obtain from having a car net of any payments they give or receive. They obtain surplus of zero if they do not own a car. The table below gives both the buyer and the seller's valuation of each type of car. Category Buyer Seller Perfect 50 46 Good 44 40 Bad 38 33 Hopeless 32 28 So, for example, if a buyer pays the price 44 for a perfect car, he obtains net surplus of 50-44-6. If a seller receives the price 48 for her hopeless car, then she obtains surplus of 48-28 = 20. The game works as follows: Simultaneously each buyer announces a price that he is willing to pay for a car. Each seller decides whether or not to sell her car (and to whom to sell it). If more than one seller accepts the price of the same buyer, then one of the sellers is randomly selected to sell the car. Find the equilibrium price (or prices) assuming that the sellers know the value of the car that they own, and buyers do not. Describe which cars are sold. A particular model of used car comes in four categories: perfect, good, bad, and hopeless. There are equal numbers of cars in each category. The market consists of at least two potential buyers and sellers of the car. Assume that there are equal numbers of buyers and sellers. All agents are interested in maximizing the expected surplus they obtain from having a car net of any payments they give or receive. They obtain surplus of zero if they do not own a car. The table below gives both the buyer and the seller's valuation of each type of car. Category Buyer Seller Perfect 50 46 Good 44 40 Bad 38 33 Hopeless 32 28 So, for example, if a buyer pays the price 44 for a perfect car, he obtains net surplus of 50-44-6. If a seller receives the price 48 for her hopeless car, then she obtains surplus of 48-28 = 20. The game works as follows: Simultaneously each buyer announces a price that he is willing to pay for a car. Each seller decides whether or not to sell her car (and to whom to sell it). If more than one seller accepts the price of the same buyer, then one of the sellers is randomly selected to sell the car. Find the equilibrium price (or prices) assuming that the sellers know the value of the car that they own, and buyers do not. Describe which cars are sold.

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In this simultaneousmove game we can analyze the equilibrium by considering the best response for bu... View the full answer