Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?

Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

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Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S (utility possibility frontier)?
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