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Economics 100C
Spring 2009
Section A00 Final Exam Solutions
QUESTION 1: 16 points
QUESTION 2: 20 points
QUESTION 3: 26 points
QUESTION 4: 20 points
TOTAL: 120 points
QUESTION 5: 20 points
QUESTION 6: 18 points
1. Consider the following twoplayer static game:
Player 2
X
Y
Z
Player 1
A
3,5
4,6
6,5
B
2,3
3,7
7,8
C
4,3
2,1
9,2
a) Does either player have a dominant strategy? Briefly explain your answer.
A dominant strategy in this static game is an action that yields a payoff that is at least as
great as any other action, regardless of which action the other player chooses. Neither
player has a dominant strategy in this example. Player 1 does best by choosing A if
player 2 chooses Y, but does best by choosing C otherwise. Each one of player 2’s three
actions is a best response to one of player 1’s three actions.
b) Which pairs of strategies represent Nash equilibria of the static game?
The Nash equilibria are the strategy pairs such that each player is choosing an action that
is a best response to the other’s action. These are stable outcomes in that neither player
would have an incentive to deviate from the equilibrium play if he/she were to learn what
the other player was planning to do. In the above game, there are two Nash equilibria:
(Player 1: A; Player 2: Y) and (Player 1: C; Player 2: X).
c) Draw the game tree associated with the sequential version of the game where player 1 moves
first and player 2 follows. Which pairs of strategies represent subgame perfect Nash equilibria of
the sequential game?
A subgame perfect Nash equilibrium (SPNE) is a pair of strategies such that each player
is choosing a best response at ever possible node in the game, regardless of whether that
node is reached or not during the course of play. This equilibrium concept is a refinement
of the Nash equilibrium concept and rules out noncredible threats. The unique SPNE
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associated with this game is (Player 1: B; Player 2: Y if A, Z if B, X if C). The payoffs
are (7,8).
2. There are only two firms producing fire extinguishers, a good that is homogenous due to
government regulations that require fire department approval before fire extinguishers can be
sold. The cost of production for firm 1 is given by
, and the cost for firm 2 is given by
. Inverse demand for fire extinguishers is given by
, where
is the
market price and
is the market quantity.
a) In attempting to maximize their profits, the two firms form a cartel. What quantity will each
firm produce?
The cartel will choose the quantities for each firm in order to maximize joint profits:
So, both firms will produce 5 extinguishers, for a market quantity of 10. Note that the
marginal costs of production for the two firms are the same (and equal to the joint
marginal revenue).
A
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 Spring '10
 Ohly
 Economics, Game Theory, best response, best response function

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