2. 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 paper 1 0 -1 scissors -1 3 0 1 (a) Show that x¹ = (₁) and y¹=(1) together are not a Nash equilibrium 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. ) together are a Nash equilibrium for (c) Show that x¹ = () and y¹ = ( this game.
2. 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 paper 1 0 -1 scissors -1 3 0 1 (a) Show that x¹ = (₁) and y¹=(1) together are not a Nash equilibrium 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. ) together are a Nash equilibrium for (c) Show that x¹ = () and y¹ = ( this game.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
qu 2
Transcribed Image Text:2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
rock paper scissors
0 -3
1
0
3
rock
1
paper
scissors -1
-1
0
(a) Show that x¹ = () and y¹ = ( ) together are not a Nash equilibrium
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) Show that x¹ = (₁,) and y¹=(,) together are a Nash equilibrium for
this game.
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