c) Consider the game having the following payoff table. Determine the value of the game and the optimal mixed strategy for each player according to the minimax criterion. Player Y Strategy 1 2 1 4 Player X 2 12
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- A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions: Weather Conditions Rain Sunshine Overcast .15 Decision .03 .55 Sun visors $-500 $-200 $1,500 Umbrellas 2,000 -900 a. Compute the expected value for each decision, and select the best one. b. Develop the opportunity loss table, and compute the expected opportunity loss for each decision.The Chinese government has created a fund worth more than 20 trillion won to foster the semiconductorindustry. Although there is a large technological difference between memory semiconductors, systemsemiconductors can be developed in a short period of time. The number of companies producinghomogeneous quality products has increased.■Question (a) In the Cournot game, when the number of firms increases from 2 to n, compare the output,total output, and profit of each firm with N.E. in the Cournot model. ■Question (b) If the number of companies participating in the semiconductor market increases to infinity,that is, in a perfectly competitive market, what will be the equilibrium point?Suppose that you watch the game show over many years and find that door #1 hides the car 50% of the time, door #2 has the car 40% of the time, and door #3 has the car 10% of the time. What then is your optimal strategy? In other words, which door should you pick initially, and then should you stay or switch? What is your probability of winning with the optimal strategy? Explain.
- 2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.The following zero-sum game has a mixed strategy: Player A al a2 a3 Player B b1 5 2 b2 -1 3 b3 2 ú -4 a) Use dominance to reduce the game to a 2x2 game b) Which strategies are dominated? c) Determine the optimal mixed strategy solution. d) What is the value of the game? 2. Interpret the solution *Please be as clear and legible as possible. Show and explain in detail all the steps. Thank you very muchGiven question is A basket of fruit is being assembled from apples, bananas, and oranges. What is the fewest number of fruit pieces that should be placed in the basket to ensure that there are at least 8 apples, 6 bananas, or 9 oranges?Your answer: The question is asking you to prepare for a worst-case scenario, not a best-case scenario. Imagine a game where you're not the one in charge of choosing the fruits - your opponent is in charge, and they don't want you to win. The opponent can get away with choosing 20 fruits (7 apples, 5 bananas, and 8 oranges) before the 21st fruit finally forces your condition to be satisfied. Therefore total required the fewest number of fruit pieces =(7+5+8)+1=21.My question:Why did you add 7+5+8 , instead of 8 apples, 6 bananas, or 9 oranges? The given is 8+6+9 not 7+5+8. Also why did you add +1? Here, you add 1: (7+5+8) +1 =21. Also, Is it pigeonhole formula? The pigeonhole is ⌈n/m⌉ not like this as far as i know. Thank you
- An engineer decides to buy four new snow tires for his car. He finds that Retailer A is offering a special cash rebate, which depends on how much snow falls during the first winter. If this snowfall is less than 50% of the mean annual snowfall for his city, his rebate will bet 50% of the list price. If the snowfall that winter is more than 50% but less than 75% of the mean annual snowfall, his rebate will be 25% of the list price. If the snowfall is more than 75% of the mean annual snowfall, he will receive no rebate. The engineer finds from a reference book that the annual snowfall for his city has a mean of 80 cm and standard deviation of 20 cm and approximates a normal distribution. The list price for the brand and size of tires he wants is $80.00 per tire. The engineer checks other retailers and finds that Retailer B sells the same brand and size of tires with the same warranty for the same list price but offers a discount of 5% of the list price regardless of snowfall that…The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this…A regional fast-food restaurant is considering an expansion program. The major factor influencing the success of such a program is the future level of interest rates. It is estimated that there is a 20% chance that interest rates will increase by 2 percentage points, a 50% chance that they will remain the same, and a 30% chance that they will decrease by 2 percentage points. The alternatives they are considering and possible payoffs are shown in the following table. Build 50 restaurants Build 25 restaurants Do nothing Rates up 2% - $220,000 -$125,000 - $60,000 Which alternative is best, based on expected value? O They should build 50 restaurants. O They should build 25 restaurants O They should do nothing. Rates unchanged Rates down 2% $55,000 $25,000 $0 $151,000 $83,000 $5,000
- Find the value of the game given the payoff matrix below and the optimal mixing strategies of both players.Suppose there are 11 buyers and 11 sellers, each willing to buy or sell one unit of a good, with values {$14, $13, $12, $11, $10, $9, $8, $7, $6, $5, $4,}. Assume no transaction costs and a competitive market. At the optimal bid, ask spread, what is the total profit that the market maker makes? $8 $12 $18 $20Answer the following questions based on the Strategy Region graph given below. When probability of high settlement is 12% and the probability of medium settlement is 40%, what is the optimal strategy? When probability of medium settlement is 20%, what is the highest probability of high settlement so that the Accept strategy to be optimal?