An owner wants to sell her car. Since she knows the car, she knows its precise...
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An owner wants to sell her car. Since she knows the car, she knows its precise quality, denoted by x. However, a potential buyer only knows that comes from a uniform distribution on the unit interval, [0, 1]. The seller is willing to sell quickly at a price not lower than 9x thousand pounds. If is known to the buyer, then the buyer will be willing to buy the car for a price not exceeding 10x thousand pounds. The seller posts a price p and the buyer either accepts or rejects it. If the car is sold, the buyer's payoff is 10x - p, and the seller's payoff is p-9x. If the car is not sold, the payoffs are zero. (Players are risk-neutral; that is, when they face uncertainty, they maximize expected payoff). (a) For what realizations of the seller's type is selling the car efficient? (b) Is there a Perfect Bayesian equilibrium which is efficient (that is, the transaction occurs if and only if it is efficient)? What is the difference between this situation and the First Welfare Theorem? (Maximum two sentences). (c) Find a Perfect Bayesian equilibrium (Hint: pay attention to strategies and the belief system). An owner wants to sell her car. Since she knows the car, she knows its precise quality, denoted by x. However, a potential buyer only knows that comes from a uniform distribution on the unit interval, [0, 1]. The seller is willing to sell quickly at a price not lower than 9x thousand pounds. If is known to the buyer, then the buyer will be willing to buy the car for a price not exceeding 10x thousand pounds. The seller posts a price p and the buyer either accepts or rejects it. If the car is sold, the buyer's payoff is 10x - p, and the seller's payoff is p-9x. If the car is not sold, the payoffs are zero. (Players are risk-neutral; that is, when they face uncertainty, they maximize expected payoff). (a) For what realizations of the seller's type is selling the car efficient? (b) Is there a Perfect Bayesian equilibrium which is efficient (that is, the transaction occurs if and only if it is efficient)? What is the difference between this situation and the First Welfare Theorem? (Maximum two sentences). (c) Find a Perfect Bayesian equilibrium (Hint: pay attention to strategies and the belief system).
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To determine the efficient outcome the sellers type needs to be considered Lets go through the questions step by step a For what realizations of the s... View the full answer
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
Posted Date:
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