Suppose you are given a mixed strategy X for player I and a mixed strategy Y for player II. Explain in your own words how you would check if (X, Y) is a saddle point in mixed strategies.
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- Burger King has introduced new strategy by reducing the price of its Whopper by 75 percent if customers also purchased french fries and a soft drink. Nevertheless, the sales dropped within two weeks. Based on your knowledge on game theory, what do you think had happened?Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.Two discount stores (Megastore and Superstore) are interested in expanding their market share through advertising. The table below depicts the strategic outcomes (profits) of both stores with and without advertising. Superstore - Advertise Superstore - Don't Advertise Megastore - Advertise $95, $80 $305, $55 Megastore - Don't Advertise $65, $285 $165, $115 When the game does reach Nash Equilibrium, the payoffs for both stores will be a) Megastore $95 and Superstore $80 b) Megastore $305 and Superstore $55 c) Megastore $65 and Superstore $285 d) Megastore $165 and Superstore $115
- Define game theory.In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.Two firms, X and Y, are planning to market their new products. Each firm can develop TV, Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix : MATRIX IS ATTACHED Find the Nash equilibria for this game, assuming that both firms make their decisions at the same time. (explain the decision step by step) If each firm is risk averse and uses a maximin strategy, what will be the resulting equilibrium? (explain the decision step by step) What will be the equilibrium if Firm X makes its selection first? If Firm Y goes first?
- Problems associated towards unique outcomes in games where multiple Nash equilibria exist”Which of the following would be best understood with game theory? Group of answer choices How two car dealerships choose prices when the prices of one dealership affects the sales of the other. A person choosing among retirement plans offered at her job The decision of what foods to buy at a grocery storeConsider the Normal Form Game characterized in the following figure: P1 \ P2 b1 b2 b3 a1 (1,2) (0,1) (0,3) a2 (3,-1) (1,1) (-1,0) a3 (2,2) (1,-1) (3,0) a4 (-5,1) (-1,0) (-3,-2) a5 (-3,3) (3,0) (2,4) What is the set of actions of player 1? O la 1, a2, a3, a4, a5) O (b1,b2, b3} O {a2, a3, a4) O (bl, b2}
- In a game of chicken, two drivers are heading towards each other on a collision course. The first one to swerve is considered the "chicken" and loses. What is the Nash equilibrium in this game? a) Both drivers swerve b) Neither driver swerves c) One driver swerves while the other doesn't d) It depends on the specificSuppose two players play the prisoners' dilemma game a finite number of times, both players are rational, and the game is played with complete information, is a tit-for-tat strategy optimal in this case? Explain using your own words.Fred and Naomi are trying to decide how to spend Sunday. Their payoffs in terms of satisfaction are below. Fred's strategy Football Naomi strategy Football Movie There is no dominant strategy Dominant strategy is football Dominant strategy is movie There is no Nash equilibrium 5,3 1,1 Movie 0,0 3,5