Problem: Random Matching Assume that the seller is matched with n e {1,2} buyers, who have common valuation of the player has a discount factor of 6. Each period the seller is randomly matched with one of the of them is randomly chosen to make an offer. If the offer is not accepted game continues, if game stops. Find the prices proposed by the seller and the buyer in equilibrium. Show that • for n = 1 if ô is close to 1, both prices are close to v; !!

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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Problem: Random Matching
Assume that the seller is matched with ne {1,2) buyvers, who have common valuation of the good v. Each
player has a discount factor of 6. Each period the seller is randomly matched with one of the buyers and one
of them is randomly chosen to make an offer. If the offer is not accepted game continues, if it is accepted,
game stops. Find the prices proposed by the seller and the buyer in equilibrium. Show that
• for n = 1
1 if 6 is close to 1, both prices are close to v;
• for n = 2 if o is close to 1, both prices are close to v.
%3D
Transcribed Image Text:2 Problem: Random Matching Assume that the seller is matched with ne {1,2) buyvers, who have common valuation of the good v. Each player has a discount factor of 6. Each period the seller is randomly matched with one of the buyers and one of them is randomly chosen to make an offer. If the offer is not accepted game continues, if it is accepted, game stops. Find the prices proposed by the seller and the buyer in equilibrium. Show that • for n = 1 1 if 6 is close to 1, both prices are close to v; • for n = 2 if o is close to 1, both prices are close to v. %3D
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