學 Consider the Domineering positions and (a) Show that both a and B are type N by finding the first move of a winning strategy for the first player and giving a brief expla- nation of how to play from there. (b) Find the types of a + a and ß + a and provide a short proof in each case. (c) Show that a # B.
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- A fast food company is offering a prize promotion game. The company claims that in 0.5 % 0.5% of all orders will receive $ 100 $100 cash, 1 % 1% of all orders will receive $ 10 $10 cash, and 10 % 10% of orders will receive a coupon for a free soft drink. The remaining orders will receive no prizes. A group of long-time customers were excited about the new promotion, and over the course of the promotion, they placed 651 orders 651 orders. Of these orders, 2 2 ended up winning $ 100 $100, 6 6 won $ 10 $10, and 52 52 won a free soft drink. The group wants to do a chi-squared goodness of fit test to test the advertised odds. Are the conditions met for this test?Consider the single object allocation problem discussed in the class. A single object needs to be allocated to one of n agents. Each agent has a value , that is, the utility he derives from the object, if given for free. The game is as follows: ? Each player/agent simultaneously announces a non-negative number - call it his bid. Denote the bid by player i as bi ≥ 0. Highest bidder wins the object - in case of a tie, the bidder with the lowest index wins (for instance, if agents 2, 3, 5 have the highest bid, then 2 wins the object). The winner gets the object for free, i.e., does not pay anything. All other agents ( i.e., those who don’t get the object) receive a payment equal to the highest bid amount. A) Formulate the game in Normal Form. B) Verify whether the game has a weak dominant strategy equilibrium. Explain why, or why not .Consider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.
- SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?A game theorist is walking down the street in his neighborhood and finds $20. Just as he picks it up, two neighborhood kids, Jane and Tim, run up to him, asking if they can have it. Because game theorists are generous by nature, he says he’s willing to let them have the $20, but only according to the following procedure: Jane and Tim are each to submit a written request as to their share of the $20. Let t denote the amount that Tim requests for himself and j be the amount that Jane requests for herself. Tim and Jane must choose j and t from the interval [0,20]. If j + t ≤ 20, then the two receive what they requested, and the remainder, 20 - j - t, is split equally between them. If, however, j + t > 20, then they get nothing, and the game theorist keeps the $20. Tim and Jane are the players in this game. Assume that each of them has a payoff equal to the amount of money that he or she receives. Find all Nash equilibria.
- A fast food company is offering a prize promotion game. The company claims that in 0.5 % of all orders will receive $100 cash1% of all orders will receive $ 10 cash and 10\% of orders will receive a coupon for a free soft drink. The remaining orders will receive no prizes. A group of long- time customers were excited about the new promotion, and over the course of the promotion, they placed 651 ordersOf these orders, 2 ended up winning $100,6 won $10 and 52 won a free soft drink. If this group wanted to do a chi-squared goodness of fit test to test the advertised odds, what would be the appropriate null and alternative hypotheses?Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random answer generator to determine which of true or false would be the correct answer for each quiz question, but his internet is not working. Instead, he writes each possible answer combination on a small slip of paper, folds each paper in half, and then places them in a box. Without looking, he draws one of the slips of paper. 4. List 5 outcomes that are in this sample space.At a certain school 60 of the 100 boys and 60 of the 80 girls signed up for the senior trip. Is there an associa-tion between going on the trip and gender? A) We can’t tell, because the class doesn’t have the samenumber of boys and girls.B) Yes, because the same number of boys and girlssigned up.C) Yes, because a lower percentage of boys signed upthan of girls.D) No, because the people on the trip were 50% boysand 50% girls.E) No, because the sign-up rate was higher among girlsthan among boys.
- A manufacturer of a robotic system a particular microchip, XG45D from 3 suppliers: Xullion electronics (30%), Sygus Systems (20%), and NESW technologies (50%). Historically, 3% of the XG45D chips from Xullion electronics have been found to be defective, 5% of the XG45D chips from Sygus System have been found to be defective, and 2% of the XG45D chips from NESW technologies have been found to be defective. When the XG45D microchips arrive at the manufacturer, they are placed randomly in a bin. A worker randomly selects the first XG45D microchip from the bin for installation in a robot and finds it defective. 1.1 What is the probability that it was manufactured by Sygus Systems? 1.2 What is the probability that it was manufactured by Xullion electronics? 1.3 Given that another XG45D microchip randomly picked from the bin by the same worker was not defective, what is the probability that it was manufactured by NESW technologies? 1.4 Suppose that the third XG45D microchip randomly picked…A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (jelly beans) for their 9:55 AM snack. Another group gets a high-protein snack (cheese) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. There is no interaction between the type of snack and the time of test μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM =…
