other small town that is served by two grocery stores, White ecide whether it will remain open on Sunday or whether it payoffs for each strategy pair are as shown in the table below Monthly Profit Payoffs Gray's Choices Open Sundays Closed Sunda 8000 700 White's Choices Open Sundays 4000 7000 Closed 10000 1200 Sundays 3000 6000 firm is the most profitable in this market?
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- You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next moveSave Answer Consider two cigarette companies, PM Inc. and Brown Inc. If neither company advertises, the two companies spit the market and earn $60 million each. If they both advertise, they again split the market, but profits are lower by $20 million since each company must bear the cost of advertisirlg. Yet if one company advertises while the other does not, the one that advertises attracts customers from the other. In this case, the company that advertises earns $70 million while the company that does not advertise earns only $30 million. What will these two companies do if they behave as individual profit maximizers? Neither company will advertise, and PM Inc. earns $60. One company will advertise, the other will not. Brown Inc. earns $70. Both companies will advertise, and PM Inc. earns $40. Both companies will advertise, and PM Inc. earns $60.Consider a small town with two competing restaurants: Doug’s Diner and Betty’s Bistro. There is 1000profit to be made in the market. Each period, the restaurants simultaneously decide whether to offer high orlow quality food. In order to offer high quality food, each restaurant must hire an expert chef, which incursan additional cost of 100. The restaurants split the profit equally if they offer the same quality of food. Ifone restaurant offers high quality food while the other offers low quality food, the high quality restauranttakes four fifths of the profit and the low quality restaurant takes one fifth of the profit.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs.(b) Determine the Nash equilibrium of this game.(c) Explain how the restaurant owners could both be better off than in the Nash equilibrium if they wereable to cooperate. Is the town as a whole better off or worse off when the firms cooperate? Why or whynot?
- Exercise A.4Explain and graphically represent the equilibria of the Cournot and Bertrand duopoly models. Indicate if they are Nash equilibria and why. Reason your answer.5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…fnan421 WWord Gozden Geç r Gorunum Varc m Ne yaomak steci gnz soy evn 1) Two firms, X and Y, are planning to market their new products. Each firm can develop either TV or Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix: FIRM Y TV LAPTOP FIRM X TV 30, 30 50, 35 LAPTOP 40,70 20, 20 A) If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be? B) Suppose both firms try to maximize profits, but Firm X has a head start in planning, and can commit first. Now what will the outcome be? What will the outcome be if Firm Y has a head start in planning and can commit first? I
- Consider following payoff matrix for two firms Firm 1 Firm 2 High Price Low Price High Price O HP O LP OLPHP 50,60 75,25 If Firm 1 follows a maximin strategy, it would choose Low Price 22,90 20,18ABC Inc. Offer Rebate No Rebate XYZ Corp Offer Rebate 20. 10 30.0 No Rebate 12.16 20,4 Which of the following is true about the game above? Lutfen birini seçin. O A Both ABC and XYZ offer a rebate as a dominant strategy OB ABC's dominant strategy is not offer a rebate, O C ABCS dominant strategy is to cffer a rebate. O D XYZE dorninant strategy is to offer a rebate.tory Bookmarks Profiles Quiz: Module 5 Qu x com/courses/111015/quizzes/852942/take To 9 7 C Tab Window Help Course Modules: Ex Topic: Planet Mon x | For the remaining questions consider two gas stations competing as an oligopoly. There are the only two gas stations in a small town. Each week they must simultaneously display their prices choosing between a high price and a low price. The payoff matrix below displays the weekly profits earned by the gas stations if they choose the various prices. Shell Decisions tv High Price Low Price Low Price NIDZA O V High Price S: $5,000 C: $5,500 (a) If Shell knows Chevron will choose the HIGH PRICE, what price should Shell choose? Low Price S: $7,500 C: $1,500 (b) If Shell knows Chevron will choose the LOW PRICE, what price should Shell choose? Low Price Aa Chevron Decisions (c) Does Shell have a dominant strategy? If so, what is it? Their dominant strategy is to Q Search Securify Module 5 Practice. x | Module 5 Lecture X (d) If Chevron knows…
- ◄ Search 12:47 PM Sun Nov 12 ← Note Nov 12, 2023 Uptown's price strategy The Nash equilibrium occurs when High Low LED RareAir's price strategy High $12 $15 The more favorable outcome would be for $12 Tt ✪ $6 B Low $6 D $8. $15 $8 S O both firms have an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell A. 92% neither firm has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell D. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell B. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell C. O the firms to collude and use the high-price strategy but this strategy requires cooperation. O one firm to take the lead and let the…3 0: she makes a pront of $9 An is ISK AVCise and aunty she makes. Let P be the probability that it rains the day of the concert. Find the number P tha makes Ann indifferent between organizing the concert in the Club or at the Park. 8. Compute the mixed strategy Nash equilibrium of the game below: Bungle F2 # Zippy E Left Right DOD F4 Up 2,-1 R I 20 F3 $ BAG 3 4 -2,0 HOT % 5 F5 Down 3,1 T 4,-2 VO MacBook Air 6 F6 Y & 7 F7 * U 8help solve The payoff matrix supplied shows outcomes of various strategies that two firms might follow in response to action on the part of the other company. This payoff matrix describes actions in developing vaccines for not-too-rare but also not-too-common diseases. Each element shows the payoffs to a set of strategies as the payoff to the domestic firm, then a comma, then the payoff to the foreign firm. Domestic firm EE ONN EN NE Enter none of these Not Enter Foreign firm Enter Not Enter Which of the outcomes in the table above are Nash equilibria? Select all that apply -[x]-[x][y],0 (EE) (EN) 0,[y] 0,0 (NE) (NN)