A seller has an indivisible asset to sell. Her reservation value for the asset is s; which she knows privately. A potential buyer thinks that the asset's value to him is b; which he privately knows. Assume that s and b are independently and uniformly drawn from [0; 1]: If the seller sells the asset to the buyer for a price of p; the seller's payoff is p-s and the buyers' payoff is b- p: 1. Suppose the buyer makes a take-it-or-leave-it offer p to the seller. What is the optimal offer if the buyers' value is b = 1/2

A seller has an indivisible asset to sell. Her reservation value for the asset is s; which she knows privately. A potential buyer thinks that the asset's value to him is b; which he privately knows. Assume that s and b are independently and uniformly drawn from [0; 1]: If the seller sells the asset to the buyer for a price of p; the seller's payoff is p-s and the buyers' payoff is b- p: 1. Suppose the buyer makes a take-it-or-leave-it offer p to the seller. What is the optimal offer if the buyers' value is b = 1/2

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.10P

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A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Is the following strategy profile a Bayesian Nash equilibrium: the buyer chooses p1 = 1/2 if b>=1/2 and he chooses p1=0 if b<1/2; the seller chooses p2=1/2 if s<1/2 and she chooses p2=1 if s>1/2. Why or why not? Can there be a Bayesian Nash Equilibrium in which the transaction price is .9 whenever there is a transaction? Why or why not?
A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p - s and the buyer's payoffis b - p. Suppose the buyer makes a take-it-or-leave-it offer p to the seller. What's the optimal offer if the buyer's value is b = 1/2?
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