Problem_set_ECOS3003_1

# Problem_set_ECOS3003_1 - Problem set ECOS3003 Due date 2pm...

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ECOS3003 Problem set 1 of 3 Problem set ECOS3003 Due date 2pm Tuesday 31 August Please keep your answers brief and concise. Excessively long and irrelevant answers will be penalised. 1 . (a) What is the definition of a Nash equilibrium? (b) What is the definition of a subgame perfect equilibrium? Consider the following game. A firm consists of a Research unit and a Manufacturing unit. The production process is as follows: the Research unit can work on either research project A1 or project A2; after observing the Research unit’s choice, the Manufacturing unit chooses to work on production line process M1 or M2. The payoffs to the parties are: 9 to the Research unit and 6 to the Manufacturing unit if they chose A1 and M1, respectively; if the Research unit chooses A1 and M2 is the choice of the Manufacturing unit the payoffs are 5 and 3 (to the Research and Manufacturing units respectively); following choices of A2 and M1 the payoffs are 7 (to Research) and 2 (to Manufacturing); and, finally, with actions A2 and M2 the payoffs are 10 (Research) and 4 (Manufacturing). (c) What are the Nash equilibria in this game? (d) What are the subgame perfect equilibria? Is this outcome surplus maximising? 2 . Two workers (workers 1 and 2) on a production line both have the choice to come to work Late or Early. If both come Late their payoffs are 5 and 4 to worker 1 and 2, respectively. If worker 1 comes Late and worker 2 comes Early the payoffs are 2 to each worker. If worker 1 comes Early and 2 comes Late the payoffs are 1 to each of them. Finally, if both workers come Early the payoffs are 3 to each worker.

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## This note was uploaded on 08/24/2010 for the course ECOS 3003 taught by Professor Andrewwait during the One '10 term at University of Sydney.

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Problem_set_ECOS3003_1 - Problem set ECOS3003 Due date 2pm...

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