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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 One '10
 andrewwait
 Game Theory, Subgame perfect equilibrium, RESEARCH UNIT

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