Problem_Set_13_solutions - Kaushik Basu Spring 2008 Econ...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Kaushik Basu Spring 2008 Econ 367 Game-Theoretic 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 400-4x. Also in terms of utility, person 1’s threat point is 20 and person two’s is 20. So now we can maximize (x-20)(400-4x-20) 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Problem_Set_13_solutions - Kaushik Basu Spring 2008 Econ...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online