midans04 - Department of Economics The Ohio State...

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Department of Economics The Ohio State University Prof. Peck February 10, 2004 Directions: Answer all questions, carefully label all diagrams, and show all work. 1. (30 points) Consider the following ±quality disclosure²game, in which a seller owns an object that has no value to her, but is valuable to a potential buyer. The value to the buyer is either $10, $20, or $30, each with probability one third. The seller observes the quality of the good (i.e., the value to the buyer), but the buyer does not observe the quality. The game starts with nature informing the seller about the quality of the good. Next, the seller decides whether or not to disclose the true quality to the buyer. That is, the buyer either observes the disclosed quality (which is known to be the truth), or else observes that quality was not disclosed. Finally, the buyer decides whether or not to buy the good at a price of $15. If the buyer does not buy, both players receive a payo/ of zero. If the buyer buys, the seller receives a payo/ of $15 and the buyer receives a payo/ equal to q 15 , where q denotes the quality of the good. (a) Draw and label the game tree. Be neat! (b) This game has several weak perfect Bayesian equilibria. Construct a WPBE in which the seller always discloses its quality. (Remember to specify beliefs as well as strategies.) (c) Construct a WPBE in which the seller never discloses its quality. (Re- member to specify beliefs as well as strategies.) Answer: For part (a), refer to the handout. We will construct a WPBE in which the seller always discloses its quality. The seller³s strategy is (D,D,D), meaning that the seller discloses when q = 10 , discloses when q = 20 , and discloses when q = 30 . The buyer³s strategy is (NB,B,B,NB), meaning that the buyer does not buy when the seller discloses q = 10 , the buyer buys when the seller discloses q = 20 , the buyer buys when the seller discloses q = 30 , and the buyer does not buy when the seller does not disclose. At all singleton information sets, the conditional probability of being at that node is one. At the buyer³s information set following no disclosure, the beliefs assign probability one to q = 10 , probability zero to q = 20 , and 1
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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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midans04 - Department of Economics The Ohio State...

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