midans03 - Department of Economics The Ohio State...

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Department of Economics The Ohio State University Midterm Answers–Econ 805 Prof. Peck 1. (30 points) Consider the following game with two players, a plainti¤ and a defendant engaged in a civil law suit. Nature moves …rst, selecting which side would win if the case goes to trial. The probability that the plainti¤ would win a trial is 1 3 , and the probability that the defendant would win a trial is 2 3 . The plainti¤ observes whether or not he would win, but the defendant does not. If the plainti¤ wins a trial, his payo¤ is 3 and the defendant’s payo¤ is ¡ 4 .I f t h e plainti¤ loses a trial, his payo¤ is ¡ 1 and the defendant’s payo¤ is 0 . Now suppose that the plainti¤, after observing who would win a trial, is forced to propose a settlement, either a low settlement, m =1 ,o rah ighse t - tlement, m =2 . The defendant, after observing the settlement o¤er but not nature’s move, must either accept the o¤er or refuse. If a settlement o¤er of m is accepted, the plainti¤’s payo¤ is m and the defendant’s payo¤ is ¡ m .I f t h e settlement o¤er is not accepted, the case goes to trial. (a) (15 points) Give the extensive form representation of this game, by drawing the game tree and labeling things properly. Try to be neat! (If I can’t readi t ,Iw i l lno tassumetha ti tisr igh t .) (b) (15 points) Find a weak perfect Bayesian equilibrium (WPBE) for this game. Remember to fully specify the strategies and the defendant’s beliefs. Explain why the conditions for a WPBE are satis…ed. Answer: (a) See the diagram. (b) The WPBE strategies are the following. The plainti¤ always o¤ers a settlement, m =2 , whether he observes that he would win at trial or he observes that he would lose at trial. The defendant rejects all settlement o¤ers, m =2 or m =1 . For the information set in which the settlement o¤er is m =2 , the defendant’s beliefs are: ¹ ( Pwins )= 1 3 and
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This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.

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midans03 - Department of Economics The Ohio State...

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