Store A and Store B compete for the business of the same customer base. Store A has 55% of the business and Store B has 45%. Both companies intend to expand to increase their market share. If both expand, or neither expand, they expect their market share to remain the same. If Store A expands and Store B does not, then Store A’s share increases to 65%. If Store B expands and Store A does not, then Store A's share drops to 50%. Determine which strategy, to expand or not, each company should take.
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- A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?
- Once your producers understand the “I WANT $3” game, you will present the “I WANT TO BE A MILLIONAIRE” game. Its rules are: There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). Each player is given $1 million at the start of the game. Independently and simultaneously, each player must choose to add to their award $0, $1, $2, $3, $4, ……$999,999, or $1,000,000. Doing so decreases the other player’s award by twice that amount. Each player ends the game with a payoff based on their initial one million, the additional amount that they announced, and the reduction due to the opponent’s announcement. The game matrix for this expanded game has 1,000,001 rows, 1,000,001 columns, and 1,000,002,000,001 pairs of payoffs. I STRONGLY RECOMMEND THAT YOU DO NOT DRAW IT! But building on what you learned in part (a), answer the following two questions: i) What is the Nash equilibrium of this game? ii) What are the Nash…Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.Youngstown-Warren Regional Airport (YNG) has had a difficult time securing passenger service from a commercial airline. a.) A few years ago, the Port Authority offered an incentive to United with guaranteed revenue equal to approximately $1.5 million, but United declined saying it was not sufficient. Suppose United anticipated that it would cost $1 million to offer flights from Youngstown, so with a guaranteed revenue of $1.5 million, their anticipated profit would equal $500,000. Given that they still chose to decline offering service from YNG, what do you know must be true? Put this in terms of implicit costs and economic profit. b.) In 2019, YNG’s only commercial carrier, Allegiant Air stopped offering service from YNG, despite the fact that it was known to be profitable. Allegiant Air’s service from YNG was known to be profitable. Why would Allegiant Air pull service from YNG even if it had been their service from YNG had been generating a profit? Note, Allegiant started…
- 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(a) Find all subgame perfect equilibria in pure strategies (if any).(b) Find all SPE where at least one of the players uses a mixed strategy (if any)The two major scooter companies in India, ABC and XYZ, are competing for a fixed market. If both manufacturers make major model changes in a year, then their percentage market share not change. Also, if they both do not make major model changes, their percentage market share remains constant. If ABC makes a major model change and XYZ does not, then ABC is able to take away a% of the market away from XYZ, and if XYZ makes a major model change ABC does not, XYZ is able to take away b% of the market away from ABC. Express this as a 2 x 2 game and solve for the optimal strategy for each of the companies.
- You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…You are a developer that has just finished writing a new game and would like to publish it with this platform’s store. You do not expect to incur in any more costs developing the product. The app store typically keeps 20% of your revenue but, in order to give an incentive to sellers, the app store will only charge 15% of revenue to successful apps selling more than 60,000 units a year, and 10% to top-selling apps with more than 85,000 units sold. Assume that there are no extra (in-game) charges beyond the price to acquire the game. Using the data in the table below, at what price should you sell your game at? (Don't forget to take into account elasticity) Quantity Price Total Revenue To Store Revenue Elasticity 96261.14 $ 0.99 $ 95,298.53 10% $ 85,768.67 -0.11 85920.32 $ 1.99 $ 170,981.43 10% $ 153,883.29 -0.24 75579.50 $ 2.99 $ 225,982.70 15% $ 192,085.29 -0.41 65238.68 $ 3.99 $ 260,302.33 15% $…There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis price