Consider the following game in strategic form. bị b2 b3 1,6 5,5 8,4 a1 6,9 7,3 a2 4,2 2,2 3,1 6,7 a3 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.) O <6,7> <3,1> O <4,2> <8,4> O <5,5> <2,2> <7,3> <6,9> <1,6>
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- Consider the following strategic game with 2 players: P1 AND P2 E F G H A 10,30 0,50 5,5 40,20 B 40,10 10,10 8,20 30,5 C 15,5 10,30 5,20 25,20 D 20,3 20,8 6,6 20,0 (a) Specify the strategies for P1 and P2, respectively. Eliminate all strictlydominated strategies, and FIND the reduced game until you can reduce the game nofurther.(b) Find all the Nash equilibria for the reduced game, including the mixed-strategy onesExercise A.2 . Sinergy and Dinaco are the only two companies in a high-tech industry. They are faced with the following matrix of results when deciding their research budget: After analizing the graph, answer the following questions... a) Does Sinergy have a dominant strategy? Reason your answer. b) Does Dinaco have a dominant strategy? Reason your answer. c) Is there a Nash equilibrium in this scenario? Reason your answer.Consider a bankruptcy game with two risk-neutral players where V = $600,000, C1 = $400,000, and C2 = $800,000. What is the Nash bargaining solution?
- Consider the following game in strategic or normal form. A2 B2 C2 A1 1,0 1,2 -2,1 B1 6,2 0,3 2,3 C1 2,2 -2,1 2,3 Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible. What is the set of rationalizable strategies for each player? What is/are Nash equilibrium(s) in this game?Consider a variation of the television station broadcast game of Exercise 4 in Chapter 7. Suppose the stations interact sequentially. First, MBC chooses between 6:00 and 7:00. Then, after observing MBC’s choice, RBC decides between 6:00 and 7:00. Finally, after observing the behavior of both MBC and RBC, CBC chooses either 6:00 or 7:00. Payoffs are as given before. Draw the extensive form of this sequential game and compute the subgame perfect equilibrium.A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
- True or False: Every finite extensive-form game of imperfect information admits at least one pure-strategy Nash equilibrium. Justify if true or give a counter-example if notConsider the following payoff matrix that is below : A. Does Player A have a dominant startegy? Explain why or why not b. Does player B have a dominant strategy? Explain why or why not. Player B Strategy 1 2 Player A Strategy 1 $2,000 \ $1,000 -$1,000 \ -$2,000 2 -$2,000 \ -$1,000 $1,000 \ $2,000Economics Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first): · (250, 290) if both firms deviate · (290, 330) if both firms cooperate · (230, 370) if only firm 2 deviates · (350, 270) if only firm 1 deviates a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated? b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?
- 10) Consider a repeated game in which the following one-shot game between two players is repeated "infinitely." Denote by "d" the discount factor. (Assume both players have the same discount factor.) Player 2 Cooperate Defect Player 1 Cooperate 5, 4 0, 5 Defect 6, 0 1, 1 The two players try to support cooperation by using "grim trigger strategy" as discussed in class. Answer YES or NO to each of the following three questions. (a) Can they support cooperation if the common discount factor, d, is equal to 0.23? (b) Can they support cooperation if the common discount factor, d, is equal to 0.4? (c) Can they support cooperation if the common discount factor, d, is equal to 0.15?Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: True or False: Only Little Kona has a dominant strategy in this game. True or False Which of the following outcomes represent a Nash equilibrium in this case? Check all that apply. Big Brew maintains a high price and Little Kona enters. a.Big Brew maintains a low price and Little Kona enters. b.Big Brew maintains a high price and Little Kona does not enter. c.Big Brew maintains a low price and Little Kona does not enter. Big Brew threatens Little Kona by saying, “If you enter, we're going to set a low price, so you had better stay out.” True or False: Little Kona should not believe the threat. True or False If the two firms could collude and agree on how to split the total profits, what outcome would they…You are considering entering a market serviced by a monopolist. You currently earn £0 economic profits, while the monopolist earns £5. If you enter the market and the monopolist engages in a price war, you will lose £5 and the monopolist will earn £1. If the monopolist doesn't engage in a price war, you will each earn profits of £2. (a) Write out the extensive form of the above game? (b) Are there any Nash equilibria for the game? Explain. (c) Is there a subgame perfect equilibrium? Explain. (d) If you were the potential entrant, would you enter? Explain why or why not.