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![Question 16
Find Iterated dominant strategy equilibrium
L CR
T|0,4 4,0 5,3
M 4,0 0,4 5,3
В 3,5 3,5 |6,6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d19bc64-a779-446d-b58a-6bb71e2e972d%2F302f83a4-8ad1-445b-9913-c46a1ec1286f%2F7q9v3rm_processed.jpeg&w=3840&q=75)
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- 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.Question 36 Consider the following normal form of a game. A D. (-3,-4) (-2,-5) (-1,0) (-4,-3) What is the maximin strategy of the row player? A O Ba W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to
- Consider the following normal form game Player 2 L C R Player 1 5,4 4, 5 3,8 8,3 8,0 8,8 5,5 6,3 0,8 UMD5. For the strategic form game shown, derive the strategies that survive the IDSDS. Player 2 y 5,2 3,4 2,1 4,4 3,2 3,3 Player 1 3,5 4,4 0,4 2,3 1,5 3,0a 12, 9, 3 m 1 N b 10, 9, 4 7" 11, 15, 1 B 10, 20, 10 What's the possible outcome of this game?
- A R1 R2 C1 5,4 6,4 B C2 11,5 9, 2 In this game between players A and B, Only A has a dominant strategy O Only B has a dominant strategy Both players have a dominant strategy O Neither player has a dominant strategyPlayer 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?1. Repeated Game Consider the following normal form game. D Player 1 E F A 10, 10 -12,-1 15, -1 Player 2 B -1, -12 8,8 -1,-1 C -1, 15 -1,-1 0,0 (a) Suppose this game is played once. Find all pure strategy Nash equilibria. (b) Now suppose the game is played two times without discounting. Find all strategy profile that can be played in the first period in a SPNE. (c) Now suppose the game is played T times without discounting, where T is a finite number. Find the smallest T such that (E,A) is played in the first period. (d) Now suppose the game is played infinitely many times and the players have a same discount factor 8 < 1. Find the smallest d that can support the SPNE in which (D,A) is played in every period along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as a punishment).
- Name: 1. Consider the following simultaneous move game: a. 2.5 4 Row Top Up Down Bottom N 16xe mszbiM Left 5,5 2,6 3,1 3,5 Column Center 8,4 10,1 5,4 9,7 Middle (6,6 2,4 3,3 4,5 Right 5,4 2,4 16 3,4 20hunini 02:hobe Use the method of iterated elimination of dominated strategies to eliminate as many strategies as possible for each player. Briefly explain your steps. (4 marks) 26 5100W sed mexa pm/ ebul b. Using the method of best responses, find the Nash Equilibrium of this game. Mark the best response on the matrix and circle the NE. Briefly explain why this is a NE. (4 marks) anatibunenk c. Consider the outcome (Bottom, Center), briefly explain why this is NOT a Nash Equilibrium. (2 marks)Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?b 500,0 -10, 30 B 6,-1 0,0 C -1, 20 -20, 100 What is the Nash Equilibrium of this game? A a a. (C, c) O b. (C, b) O c. (A, a) O d. (B, b) C 20, 12 8, -2 7,800
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