Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors гock 0. -3 1. 0. раper scissors -1 (a) Show that xT= (,) and yT= (;,) together are not a Nash equilibrium 3 3 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors гock 0. -3 1. 0. раper scissors -1 (a) Show that xT= (,) and yT= (;,) together are not a Nash equilibrium 3 3 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
Chapter15: Oligopoly And Strategic Behavior
Section: Chapter Questions
Problem 17P
Related questions
Question
![Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
rock paper scissors
rock
0.
-3
1
1.
раper
scissors
-1
-1
3
(a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium
3'31
for this modified
3'3
game.
(b) Formulate a linear program that can be used to calculate a mixed strategy
x € A(R) that maximises Rosemary's security level for this modified
game.
(c) Solve your linear program using the 2-phase simplex algorithm. You should
use the format given in lectures. Give a mixed strategy x E A(R) that has an
optimal security level for Rosemary and a mixed strategy y E A(C) that has
an optimal security level for Colin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc42a90ac-0cbc-4693-969e-627d957bc11a%2Fb255ab97-c437-4382-b3cd-fb2a0fffb72c%2Fkybdz1q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
rock paper scissors
rock
0.
-3
1
1.
раper
scissors
-1
-1
3
(a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium
3'31
for this modified
3'3
game.
(b) Formulate a linear program that can be used to calculate a mixed strategy
x € A(R) that maximises Rosemary's security level for this modified
game.
(c) Solve your linear program using the 2-phase simplex algorithm. You should
use the format given in lectures. Give a mixed strategy x E A(R) that has an
optimal security level for Rosemary and a mixed strategy y E A(C) that has
an optimal security level for Colin.
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