This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problem Set 2 (Lecture 2, March 9) ECOS3012  Strategic Behavior, Semester 1, 2011 Note. I have given a number of problems here concerning the Nash Bargaining Solution and on taking a noncooperative game situation and representing it as a strategic/normal form game. Some of these give you practice and others anticipate what I will teach in the next class. I do not obviously expect you to solve all the problems by next week, but I do expect you to have tried enough of them by the time I go over their solutions in next week’s (16 March) class. Calculating Nash Bargaining Solutions 1. ( Bargaining over a pie of unit size ) In class, we studied how to compute the Nash Bargaining Solution when splitting a pie of unit size and the utilities of a player from getting x units of the pie is u 1 ( x ) = x if it is Player 1 and u 2 ( x ) = √ x if it is Player 2. ( d 1 = d 2 = 0 was assumed.) Now, replace the utility functions with u 1 ( x ) = x α and u 2 ( x ) = x β where 0 < α,β < 1. (a) Compute the Nash Bargaining solution. How does the solution vary with respect to α and β ? (b) If you are familiar (from other your past courses) with how α, β determine risk attitudes, does being relatively more risk averse benefit you or hurt you? Does this feel intuitive? (Do not worry if you cannot answer this. I will explain when I go over the solutions.) 2. The profit of a firm when a worker works for ` hours at an hourly wage of w is u 1 ( w,` ) = 8 √ ` w` . The payoff of a worker in that case is u 2 ( w,` ) = w` + (24 ` )....
View Full
Document
 Spring '11
 etw

Click to edit the document details