1
Economics 1200
Spring 2012
Homework # 2
Write your answers to the following questions on separate sheets of paper. Your answers are due
in class on
Tuesday, February 7
.
Late homeworks are not accepted.
1.
Consider the tworound home bargaining game discussed in class. The minimum the
seller will sell his home for is $188,000 and the maximum the buyer is willing to pay is
$200,000.
Both players know these two amounts and are bargaining over the difference,
M=$12,000. Assume the disagreement values are 0 for both players.
Suppose the buyer
moves first by making a proposal and the seller can accept or reject it. If the seller rejects
the buyer’s proposal, the seller gets to make a counterproposal, which the buyer can then
accept or reject. The game is then over. Suppose that both players discount future income
using a period discount factor of
=.2.
a.
Use rollback to find the equilibrium for this 2round game. What is the sale price
of the home?
Which player buyer or seller gets the larger share of M?
b.
Suppose the buyer’s discount factor was
b
=.8 while the seller’s discount factor
remained at
s
=.2?
How does your answer to part a change in this case?
c.
Return to the case where both have the same discount factor of
=.2. Suppose
now that there is no limit to the number of alternating bargaining rounds and the
buyer continues to move first.
Use rollback reasoning to find the equilibrium
price in this case. How does an unlimited number of bargaining rounds affect the
share of the first mover—the buyer—relative to the 2 or 3round case? What
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Game Theory

Click to edit the document details