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Unformatted text preview: Econ 100C Practice Midterm #2  Answer Key Question 1 Consider the following sequential game with two stages: A single seller o ers a good to a single buyer. In the rst stage of the game, the buyer can choose between three di erent strategies: o er $20 for the good, o er $40, or o er $60. In the second stage, the seller can accept or refuse the o er. The seller values the good at $32. If she does not sell the good, her payo is zero. The buyer values the good at $45, and his payo is zero if the seller rejects his o er. a) Draw the game tree. First, we need to gure out the payo s for the game. If a sale occurs, the buyers pay o will be his value of the item minus the price he pays. The sellers payo will be the price she receives minus her value of the item. If a sale does not occur, both players payo s are zero. We can now draw the game tree as below: b) Find the subgame perfect Nash Equilibrium of the game. We can solve for the subgame perfect Nash Equilibrium by backwards induction. Start with the sellers decision. The sellers response to each of the buyers three potential o ers is a subgame. Since the seller is just comparing her payo from accepting the o er to her payo from rejecting the o er, solving each subgame is very simple. Subgame 1: buyer o ers $20. In this subgame, the sellers payo from accepting is $12 dollars while her payo from rejecting is $0. Therefore, the seller will reject the o er in this case, getting a payo of $0. This means that the buyer can expect a payo of $0 if he o ers $20. Subgame 2: buyer o ers $40. In this subgame, the sellers payo from accepting is $8 dollars while her payo from rejecting is $0. Therefore, the seller will accept the o er in this case, 1 getting a payo of $8. This means that the buyer can expect a payo of $5 if he o ers $40. Subgame 3: buyer o ers $60. In this subgame, the sellers payo from accepting is $28 dollars while her payo from rejecting is $0. Therefore, the seller will accept the o er in this case, getting a payo of $28. This means that the buyer can expect a payo of $15 if he o ers $60. Initial decision: how much to o er? Now that we know the buyers payo s from each o er he might make, we can select the best one. Therefore, the buyer o ers $40, the seller accepts the o er, and the buyer earns $5. That means of subgame perfect Nash Equilibrium is [(O er $40), (Reject if o er = $20, Accept if o er = $40, Accept if o er = $60)]. c) Now, assume that the order of the moves is reversed. In the rst stage, the seller can o er the good for $20, $40 or $60, and in the second stage, the buyer can accept or refuse the o er. Draw the new game tree and nd the subgame perfect Nash Equilibrium....
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This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.
 Spring '10
 Ohly
 Economics

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