1. Nash Equilibrium(a) Find all pure Nash EquilibriaP1/P2 WX Y Z9,90,75,51,17,00,0 4,2 7,75,52,4 0,0 1,11,1 7,7 1,1 0,0ABCD(b) Consider the following picnic game. There are N players in the gameeach 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. Ifthey decide to bring food it comes at a cost c;(1) = 1 and no cost tobring food. Payoffs are sum of food brought minus individual cost.i. Write out the normal form matrix if N = 2ii. If N = 2 find all pure Nash Equilibriaiii. Find all pure Nash Equilibria in the general game

Nash equilibrium, no player has an incentive to unilaterally deviate from their chosen strategy, as…

Answered: (a) Find all pure Nash Equilibria P1/P2…

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(a) Find all pure Nash Equilibria P1/P2 W 9,9 7,0 5,5 1,1 A B C D X Y Z 0,7 5,5 1,1 0,0 4,2 7,7 2,4 0,0 1,1 7,7 1,1 0,0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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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

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