prob2 - Problem Set 2 (Lecture 2, March 9) ECOS3012 -...

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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 non-cooperative 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- ` )....
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prob2 - Problem Set 2 (Lecture 2, March 9) ECOS3012 -...

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