ECOS3012 Strategic Behaviour
Tutorial 5
Q1easier Three oligopolists operate in a market with inverse demand given by P(Q) = a−Q, where
Q = q1+q2+q3 and qi is the quantity produced by firm i. Each firm has a constant marginal
cost of production, c, and no fixed cost. The firms choose their quantities as follows:
(1) firm 1 chooses q1 ≥ 0
(2) firms 2 and 3 observe q1 and then simultaneously choose q2 and q3, respectively.
What is the subgame-perfect outcome?
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Q2 The accompanying simultaneous-move game is played twice, with the outcome of the first
stage observed before the second stage begins. The payoff of the repeated game the sum of
the payoffs from the two stage games. The variable x is greater than 4, so that (4, 4) is not
an equilibrium payoff in the one-shot game. For what values of x is the following strategy
profile a subgame-perfect Nash equilibrium?
Play (Q,Q) in the first stage.
If the first-stage outcome is (Q,Q), play (P,P) in the second stage.
If the first-stage outcome is (y,Q) where y 6= Q, play (R,R) in the second stage.
If the first-stage outcome is (Q,z) where z 6= Q, play (S,S) in the second stage.
If the first-stage outcome is (y,z) where y 6= Q and z 6= Q, play (P,P) in the second
stage.
Player 2
P Q R S
Player 1
P 2, 2 x, 0 -1, 0 0, 0
Q 0, x 4, 4 -1, 0 0, 0
R 0, 0 0, 0 0, 2 0, 0
S 0, -1 0, -1 -1, -1 2, 0
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Q3. The simultaneous-move game below is played twice, with the outcome of the first stage ob-
served before the second stage begins. The payoff of the repeated game the sum of the
payoffs from the two stage games. Can the payoff (4, 4) be achieved in the first stage in a
pure-strategy subgame-perfect Nash equilibrium? If so, give strategies that do so. If not,
prove why not.
L C R
T 3, 1 0, 0 5, 0
M 2, 1 1, 2 3, 1
B 1, 2 0, 1 4, 4
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