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201FinalAnswers-2006spring

201FinalAnswers-2006spring - SABANCI UNIVERSITY ECON 201 B...

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SABANCI UNIVERSITY ECON 201 – B GAMES AND STRATEGY FINAL EXAMINATION June 13, 2006 Instructor: Mehmet Baç Time allowed: 100 minutes, 114 points READ CAREFULLY... 1. ( 30 points ). Mr Opus is becoming an academician. He has two potential types: he likes teaching (type-T) with probability 0.5 or he likes research (type-R) with probability 0.5. He knows his type privately. Mr. Opus will move first and choose between two actions, excel in teaching and excel in research. For type-T of Mr Opus, the cost of excelling in teaching is zero, while the cost of excelling in research is 500TL. For the type-R, excelling in research is costless while excelling in teaching costs 500TL. Next, the University of Orhanli (UO),who does not know Mr. Opus’ type, will observe the excellence choice and offer a salary denoted W R if Opus excels in research, W H if Opus excels in teaching. Mr Opus may accept or reject the offer, and the game ends. UO gets the benefit 2000 TL from a type-R who excels in research, 2500 TL from a type-R who excels in teaching. UO gets the benefit 3500 TL from a type-T academician who excels in research, 2500 TL from a type-T who excels in teaching. When it makes an accepted salary offer, UO’s payoff is: Benefit – Salary (W), Mr Opus’ payoff is: Salary (W) – excellence cost (500 or 0) . If the offer is rejected , UO gets zero, and Mr Opus gets the payoff 1000TL – excellence cost (500 or 0) if he is of type-R , 1500 - excellence cost (500 or 0) if he is of type-T . (NOTE: THE FIRST PAYOFF IS MR OPUS’ PAYOFF, which is the opposite of the usual order of payoffs!) (2000- W R , W R ) ( 2500- W H , W H -500) yes W R {μ} excel res. type-R excel teach.{β} yes W H { 0.5 } ( 0 , 1000) No No ( 0 , 500 ) UO Nature UO ( 3500- W R , W R -500 ) { 0.5 } yes yes ( 2500- W H , W H ) W R excel res. type-T excel teach W H No (0 , 1000) No (0 ,1500) (i) [5p] Copy the extensive form of the game to your paper and fill in the question marks . (ii) [5p] How does UO’s offer strategy depend on its updated beliefs (μ and β, after observing excellence choice of Mr Opus)? (iii) [10p] Is there a separating equilibrium in which type-R of Mr Opus chooses to excel in research while type-T chooses to excel in teaching? Verify and write the strategies if you find an equilibrium.
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