Question 39 Normal Form Game: The table below provides a normal form, 2 x 2 game. The players are Column and Row. Column can choose either LEFT or RIGHT, and Row can choose either UP or DOWN. Their payoffs for each combination of moves are provided in the four boxes. Column Row LEFT RIGHT -2 7 UP -9 4 -7 DOWN -5 -6 In the above game, the Row player has a dominant strategy. OA. True 1
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- In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game. = Win a prize = Do not win a prize 1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link below. Click to view hint 2. Create the probability distribution of the game. Fill in the missing parts of the chart. x → Number of Red Chips P(x) Result 1 Lose + Win + 3. Now find the expected value. x, Number of red chips X → Net Money Won or Lost P(x) 1 2$ 4. What is the expected Value? MacBook Air D00 F3 F4 F5 F7 F8 $ * 4 5 7 8 9 6.Consider the game described by the following table. What is the best response for the column player if s/he knows that the row player will make the Y move? B OA O C ROW PLAYER O There is no definitive answer. X Y COLUMN PLAYER A 4, -1 3, -1 B -1,0 -2,4 C 2,1 0,2In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game. = Win a prize = Do not win a prize 1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link below. Click to hide hint CHIP 1 CHIP 2 Probability P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 0.5 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25 Start 0.5 0.5 P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25
- 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.Given 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 youConsider the following game. Two construction firms are thinking about bidding cable stayed bridge in one of the lakes near to Warangal. The take from the bridge construction would be Rs. 20 lakhs each, but the job requires two firms (one to design and one to build the structure). Each firm could instead build apartment in smart city project. The take from apartment in smart city project is only Rs. 5 Lakhs but can be done with one firm acting alone. i. Write down the payoff matrix for this game. ii. What are the strategies for this game? ii. What are the equilibria for this game?.
- Consider the game having the following normal form. In applying IESDS, which of the following strategies of the row player will be eliminated? COLUMN PLAYER A 6, 5 -5, 11 7,9 ROW PLAYER Y 10, 6 7, 10 11, 9 11, 7 -4, 11 8, 4 W 11, 3 -1, 10 8, 8 X.Consider the game that starts with a pile of eight stones and the players take turns re- moving one, two, or three stones from the pile. The player who removes the last stone looses. (a) Draw the game tree for this game. (b) Determine which player has a winning strategy.You are going to play the 7-11 game, which has the following rules: You roll two dice. If the total value of the two dice is 7 or 11, you immediately win the game. If the total value is 2, 3, or 12, you immediately lose. If the total value is 4, 5, 6, 8, 9, or 10, you keep this value as a referenced point. Then, you continue rolling the dice until you obtain the same value as the referenced point then you win the game. However, if you obtain the value of 7 before the referenced point, then you lose. For example, you obtain 4 in the first time of rolling, you keep rolling the dice until you get 4 (before 7) then you win. Similarly, you obtain 4 in the first time of rolling, you keep rolling the dice but you get 7 (before 4) then you lose. What is the probability to win this game? You can solve this question either by - a simulation - in this case you have to answer one more question, i.e., on average how many times do you roll the dice for each game? (for a submission, you will need to…
- A particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.Zara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game.