1. In the following payoff matrix, each firm has two possible strategies, and must move simultaneously. Assuming that each knows only its own payoff structure, what decision would each firm make? Is this a Nash equilibrium? Suppose each player can see the entire payoff structure instead of only its own. How would this affect Firm 2? Payoffs shown are (Firm 1, Firm 2): Firm 2 B A 3,1 2,0 Firm 1 B 2,4 1,5

Exploring Economics
8th Edition
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter15: Oligopoly And Strategic Behavior
Section: Chapter Questions
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Please help for these 3 questions with detail explanation. Thank you so much.

1. In the following payoff matrix, ezch firm has two possible strategies, and must move
simultaneously. Assuming that each knows only its own payoff structure, what decision would
each firm make? Is this a Nash equilibrium? Suppose each player can see the entire payoff
structure instead of only its own. How would this affect Firm 2? Payoffs shown are (Firm 1, Firm
2):
Firm 2
A
3, 1
2,0
Firm 1
2,4
1,5
2. In the following game, players must move simultaneously. How many Nash equilibria are there?
Which will occur without collusion? Which will occur if collusion is allowed? (Collusion means if
they make contract to identify firms' strategy before game is played.)
Firm 2
A
3,1
7,0
Firm 1
B
2,4
5,3
3. Find the dominant and daminated strategies in the following games (in case
players have such strategies). Is there any dominant strategy equilibrium in
any of these games?
(a)
Player 2
LR
Player 1 U 5,5 3,6
D 6,3 4,4
(b)
Player 2
X Y Z
A 2,5 4,4 5,5 0,4 1,5
B 5,3 3,3 4,3 2,2 1,0
Player 1 C 6,0 3,0 1,1 1,1 0,1
D 6,2 3,0 4,2 | 3,2 1,2
E 1,1 5,1 4,2 | 1,0 0,2
V
Lightshot Screenshot
Transcribed Image Text:1. In the following payoff matrix, ezch firm has two possible strategies, and must move simultaneously. Assuming that each knows only its own payoff structure, what decision would each firm make? Is this a Nash equilibrium? Suppose each player can see the entire payoff structure instead of only its own. How would this affect Firm 2? Payoffs shown are (Firm 1, Firm 2): Firm 2 A 3, 1 2,0 Firm 1 2,4 1,5 2. In the following game, players must move simultaneously. How many Nash equilibria are there? Which will occur without collusion? Which will occur if collusion is allowed? (Collusion means if they make contract to identify firms' strategy before game is played.) Firm 2 A 3,1 7,0 Firm 1 B 2,4 5,3 3. Find the dominant and daminated strategies in the following games (in case players have such strategies). Is there any dominant strategy equilibrium in any of these games? (a) Player 2 LR Player 1 U 5,5 3,6 D 6,3 4,4 (b) Player 2 X Y Z A 2,5 4,4 5,5 0,4 1,5 B 5,3 3,3 4,3 2,2 1,0 Player 1 C 6,0 3,0 1,1 1,1 0,1 D 6,2 3,0 4,2 | 3,2 1,2 E 1,1 5,1 4,2 | 1,0 0,2 V Lightshot Screenshot
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