Exploring Economics
8th Edition
ISBN: 9781544336329
Author: Robert L. Sexton
Publisher: SAGE Publications, Inc
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Chapter 15, Problem 15P
To determine
To find:
The dominant strategy for the given payoff matrix.
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Consider the Normal Form Game characterized in the following figure:
P1\P2 X Y Z
A
B
с
(1,1) (0,0) (-1,0)
(0,0) (2,2) (0,0)
(0,-1) (0,0) (3,3)
Which is the Strictly Dominated Strategy for player 1?
O (1,0,0)
O (0,1,0)
O (0,0,1)
There are no strictly dominated strategies for player 1
Consider the two-stage, static game depicted in Figure 5.1 involving two companies that enter into
an agreement to maximize total profits. The payoffs in this game are in millions of dollars. The
optimal strategy for both firms is to:
Firm Y
A
C
(3, 3)
(1, 1)
(1, 1)
Firm X
(1, 1)
(5, 5)
(7, 4)
C
(1, 1)
(4, 7)
(6, 6)
Payoffs: (Firm X, Firm Y)
FIGURE 5.1
O Play B in stage 1 and stage 2.
O Play B in stage 1 and play A in stage 2.
O Play C in stage 1 and stage 2.
O Play B in stage 1 and play C in stage 2.
O Play C in stage 1 and play B in stage 2.
Consider a Cournot duopoly. The inverse demand function of the
market is given by p = 10-Q, where p is the market price, and
Q = 91 +92 is the aggregate output. The marginal costs of the two
firms are C₁
1 and C₂ = 4.
=
(a) Solve for the Nash equilibrium of the game including firm out-
puts, market price, aggregate output, and firm profits.
(b) Now suppose these two firms play a 2-stage game. In stage 1,
they produce capacities 9₁ and 92, which are equal to the Nash
equilibrium quantities of the Cournot game characterised by part
(a). In stage 2, they simultaneously decide on their prices p₁ and
P2. The marginal cost for each firm to sell up to capacity is 0. It
is impossible to sell more than capacity. The residual demand for
10 Piāj if Pi > Pj
firm ij, is Di (Pi, Pj)
=
10-Pi
2
=
if pipi. (Note,
if Pi < Pj
10 - Pi
here we assume that the efficient/parallel rationing applies).
Prove that it is a Nash equilibrium of the second stage subgame
that each firm charges the market clearing…
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