b) Two players, both with zero wealth, bargain over how to divide £X > 0 between them. Failure to reach agreement means both get nothing. Both players are expecled utility max- imisers. Player 1 has utility u(x) = x", where 0 < a < 1. Player 2 has utility u(x) = x, where 0< B <1. Determine the Nash solution for this problem and discuss.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.6P
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b) Two players, both with zero wealth, bargain over how to divide £X > 0 between them.
Failure to reach agreement means both get nothing. Both players are
expecled utility max-
imisers. Player 1 has utility u(x) = x", where 0 < a < 1. Player 2 has utility u(x) = x',
where 0 < B < 1. Determine the Nash solution for this problem and discuss.
%3D
Transcribed Image Text:b) Two players, both with zero wealth, bargain over how to divide £X > 0 between them. Failure to reach agreement means both get nothing. Both players are expecled utility max- imisers. Player 1 has utility u(x) = x", where 0 < a < 1. Player 2 has utility u(x) = x', where 0 < B < 1. Determine the Nash solution for this problem and discuss. %3D
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