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Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: (a) Show that x¹ = rock paper scissors 0 -3 rock paper 1 scissors -1 for this modified game. 0 3 -1 1 1 (,,) and y¹ = (½, ½, ½) together are not a Nash equilibrium

Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: (a) Show that x¹ = rock paper scissors 0 -3 rock paper 1 scissors -1 for this modified game. 0 3 -1 1 1 (,,) and y¹ = (½, ½, ½) together are not a Nash equilibrium

Advanced Engineering Mathematics
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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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 paper scissors 0 -3 1 -1 0 3 1 1 1 (a) Show that x¹ (½, ½, ½) and y¹ = (3½, ½, ½) together are not a Nash equilibrium for this modified game. 3' 3' 3. -1 0 (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 = (½, ½, ½) and y¹ = (², 1, 2) together are a Nash equilibrium for this game. י י
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 paper scissors 0 -3 1 -1 0 3 1 1 1 (a) Show that x¹ (½, ½, ½) and y¹ = (3½, ½, ½) together are not a Nash equilibrium for this modified game. 3' 3' 3. -1 0 (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 = (½, ½, ½) and y¹ = (², 1, 2) together are a Nash equilibrium for this game. י י
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