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- 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?Consider the game having the following normal form. Which of the following strategies of the column player dominates other strategies? COLUMN PLAYER A C 6, 5 -5, 11 7,9 ROW PLAYER Y 10, 6 7, 10 11, 9 11, 7 -4, 11 8,4 W 11, 3 -1, 10 7,8 C O A B.
- 20) Given the payoff matrix in the figure, the Nash equilibrium outcome of this game is for: Ajinomoto Produce 30 Produce 40 million pounds million pounds Ajinomoto makes $180 million Ajinomoto makes $200 million Produce 30 million ADM makes $180 million ADM makes $150 million pounds Ajinomoto makes $150 million Ajinomoto makes $160 million Produce 40 million ADM makes $200 million ADM makes $160 million pounds O A. each firm to produce 30 million pounds. B. each firm to produce 40 million pounds. C. ADM to produce 30 million pounds and for Ajinomoto to produce 40 million pounds. D. ADM to produce 40 million pounds and for Ajinomoto to produce 30 million pounds. ADM1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?(2) Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below. Firm 2 A В C -10, -10 10, 0 20, 10 0, 10 -20, -20 15, -5 10, 20 -5, 15 -30, -30 А Firm 1 B C a. Are there any Nash equilibria in pure strategies? If so, what are they? b. If both firms use maxmin strategies, what outcome will result? c. If Firm 1 uses a maxmin strategy and Firm 2 knows this, what will Firm 2 do?
- 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.12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?6. Consider the following two-player game: 2 L M U 3,3 2,3 1 M 2,1 3,1 D R 0,2 3,3 0,3 3,0-5, -5 a. Find all pure NE. b. Find a (non-pure) MNE in which player 1 (the row player) plays a pure strategy. c. (Harder Question) Show that there cannot be a CE prescribing that strat- egy D of player 1 (the column player) is played with positive probability.
- 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?Consider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium O Hawk, Dove O Dove, Hawk O Hawk, Hawk O Hawk, HawkHelp me please
