Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![1. Nash Equilibrium
(a) Find all pure Nash Equilibria
P1/P2 W
X Y Z
9,9
0,7
5,5
1,1
7,0
0,0 4,2 7,7
5,5
2,4 0,0 1,1
1,1 7,7 1,1 0,0
A
B
C
D
(b) Consider the following picnic game. There are N players in the game
each who can chose to bring food to the picnic or not. Let b;= {0, 1}
be player i's choice of bringing food with 0 as not and 1 as yes. If
they decide to bring food it comes at a cost c;(1) = 1 and no cost to
bring food. Payoffs are sum of food brought minus individual cost.
i. Write out the normal form matrix if N = 2
ii. If N = 2 find all pure Nash Equilibria
iii. Find all pure Nash Equilibria in the general game](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37105433-7edd-4cf4-bd81-8587ee1a9a62%2F58602dc2-f30c-4424-873e-a1b91035c9cf%2Fapb2kfm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Nash Equilibrium
(a) Find all pure Nash Equilibria
P1/P2 W
X Y Z
9,9
0,7
5,5
1,1
7,0
0,0 4,2 7,7
5,5
2,4 0,0 1,1
1,1 7,7 1,1 0,0
A
B
C
D
(b) Consider the following picnic game. There are N players in the game
each who can chose to bring food to the picnic or not. Let b;= {0, 1}
be player i's choice of bringing food with 0 as not and 1 as yes. If
they decide to bring food it comes at a cost c;(1) = 1 and no cost to
bring food. Payoffs are sum of food brought minus individual cost.
i. Write out the normal form matrix if N = 2
ii. If N = 2 find all pure Nash Equilibria
iii. Find all pure Nash Equilibria in the general game
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