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Kaushik Basu
Spring
2008
Econ 367
GameTheoretic Methods
Problem Set 13
1.
Suppose two players, 1 and 2, are engaged in the following Nash bargaining
problem.
Player 1 is given (by the king) 100 bushels of wheat and asked to share
this with person 2.
If they fail to reach an agreement, the king takes away the 80
bushels from player 1 (i.e., leaves her with 20 bushels), gives 5 bushels to player
2 and destroys the rest.
(a)
Assume player 1 gets 1 util from each bushel of wheat and player 2 gets 4
utils from each bushel.
If the two players solve the problem using the
Nash bargaining solution, how many bushels of wheat will player 2 get?
Answer:
If person 1’s utility is x bushels, person 2’s utility is 4004x.
Also in terms of
utility, person 1’s threat point is 20 and person two’s is 20.
So now we can
maximize (x20)(4004x20) for x.
The answer is 57.5.
Then person two gets
42.5.
(b) Suppose all the assumptions in (a) hold, excepting for the fact that person 1
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 Spring '08
 BASU

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