C D E A. B. с 2, 2 3, 3, 0,0 C. -1 Which of the following is FALSE about the game illustrated? D -1, 3 0,0 0,0 1.1, 1.1 E 0,0 0,0 There are multiple subgame perfect equilibrium The maximum aggregate payoff (of two players) in a subgame perfect equilibrium in pure strategies is 3.1+3.1=6.2 The minimum aggregate payoff (of two players) in a subgame perfect equilibrium in pure strategies is -1+-1 -2

C D E A. B. с 2, 2 3, 3, 0,0 C. -1 Which of the following is FALSE about the game illustrated? D -1, 3 0,0 0,0 1.1, 1.1 E 0,0 0,0 There are multiple subgame perfect equilibrium The maximum aggregate payoff (of two players) in a subgame perfect equilibrium in pure strategies is 3.1+3.1=6.2 The minimum aggregate payoff (of two players) in a subgame perfect equilibrium in pure strategies is -1+-1 -2

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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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 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.
rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 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.
Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?
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