Question

1. Buyer-Seller Game. A seller of a used car wants to sell it to a prospective buyer. The seller first decides whether to repair the car hidden defects or not. Then she decides whether to charge a low price pl or a high price Ph. The buyer does not observe sellers' decision about repairing the car. After being offered a price by the seller, he decides whether to buy the car and pay the price or not. The payoff to the seller is the difference between the price and the cost of repairs c ( if she does not repair the car. The payoff to the buyer is zero if he does not buy the car; while it is the difference between the value of the car and the price paid if he buys it. The value of a repaired car is Oh while it is O L < Oh when no repairs are done. (a) Derive the extensive form of the game. (b) Define the space of strategies for each player. (c) Derive the normal form (i.e., its matrix representation). 2. Consider the following game tree: H Н, AO-- h/ \t h/ \t h/ \t h/ \t (2,1) (0,0) (0,0) (1.2) (2,1 (0,0) (0,0) (1,2) (a) List all the information sets of each player. (b) Define the strategy space of each player. (C) Does this game satisfy perfect recall? Explain.

Answer 1

Q1. (As per HOMEWORKLIB RULES I will only answer this question)

a) Given the information in the question, the extensive form can be represented as follows:-

b) The strategy spaces for the players are the following

For the Seller:-

For the Buyer

c)

		Buyer
Seller		Buy	Not Buy
	(Repair, pH)
	(Repair, pL)
	(Not Repair, pH)
	(Not Repair, pL​​​​)