midexam - Ecos3012 Strategic Behavior Midterm Exam,...

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Unformatted text preview: Ecos3012 Strategic Behavior Midterm Exam, Semester 1, 2011 NOTE: This exam consists of 20 multiple choice questions and 2 problems. Each multiple choice question is worth 3 points and each problem is worth 20 points. Therefore, you can score a maximum of 100 points. Your score in this exam is worth 35% of the final grade. Duration: 2 hours including reading time. 1. Multiple Choice Questions Instructions. • For each of the following, choose the best answer and mark it on the supplied answer sheets. • Those questions marked with a “ ? ” may require a bit more computation than others. You might consider answering those later. • Throughout, assume that in finite strategic form games, players do not use mixed strategies unless specified otherwise. 1. Suppose there are three states of the world and a typical action is given by a triple ( x,y,z ), denoting the monetary reward in the three states of the world. Consider two actions A = ( x,y,z ) and B = (ˆ x, ˆ y,z ). ( Both actions give the same reward in state 3). Now consider any other actions C = ( x,y,z * ) and D = (ˆ x, ˆ y,z * ) obtained from A and B by changing the reward in state 3. Suppose a Decision Maker (DM) is known to satisfy Expected Utility Hypothesis and it is known that she strictly prefers A to B. (a) • DM must strictly prefer C to D. (b) DM may strictly prefer C to D but depends on the value of z * . (c) DM may prefer C to D but this depends on payoffs in the first two states (d) None of the above. Solution : This is straightforward. If the Expected utility hypothesis holds, then there must be a probability distribution ( p 1 ,p 2 ,p 3 , and a utility function u such that U ( A ) = p 1 u ( x ) + p 2 u ( y ) + p 3 u ( z ) (1) U ( B ) = p 1 u ( x ) + p 2 u ( y ) + p 3 u ( z ) (2) U ( C ) = p 1 u ( x ) + p 2 u ( y ) + p 3 u ( z * ) (3) U ( D ) = p 1 u ( x ) + p 2 u ( y ) + p 3 u ( z * ) (4) It is clear that U ( A ) > U ( B ) if and only if U ( C ) > U ( D ). Ecos3012 Strategic Behavior, Midterm Exam, 2011 1 2. Consider a bargaining problem h S,d 1 ,d 2 i such that whenever a payoff vector ( u,v ) for the two players is feasible, then ( v,u ) is also feasible. Assume that Nash bargaining solution is applicable. (a) The Nash bargaining solution ( u * ,v * ) must be such that u * = v * . (b) The Nash bargaining solution ( u * ,v * ) cannot be such that u * = v * . (c) We must have log( u * ) = log( v * ). (d) • None of the above. Solution : It is tempting to say u * = v * thinking that the bargaining problem is symmetric – however we do not know that it is symmetric. For that, in addition to the given information, we need to know that the outside options are equal, i.e. d * 1 = d * 2 ....
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This note was uploaded on 08/20/2011 for the course ECON 101 taught by Professor Etw during the Spring '11 term at Università di Bologna.

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midexam - Ecos3012 Strategic Behavior Midterm Exam,...

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