For the game given above, ((p1.p2.p3).(q1.q2.q3) is a mixed strategy: The first triplet is Player 1's probability allocations to X1, X2, X3. The second triplet is Player 2's probability allocations to Y1, Y2, Y3. Which of the following is true? O a. For Player 2, Y1 is strictly dominated by Y2 Ob. ((p1.p2.p3).(q1.q2.q3)- (2/5.2/5,1/5),(3/5.1/5,1/5) is a mixed NE O. No action is strictly dominated by any mixed strategy O d. (pl.p2.p3).(qt.42.93)- (1/4.2/4,1/4,(3/4,0,1/4) is a mixed NE
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- For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea. not manufactured in Japan. is a white car, given that it was manufactured in America. Are the events ‘Korea’ and ‘Black’ Mutually Exclusive? Justify your response. Are the events ‘Korea’ and ‘Black’ Independent? Justify your responsen people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100True/False a. Consider a strategic game, in which player i has two actions, a and b. Let s−i be some strategy profile of her opponents. If a IS a best response to s−i, then b is NOT a best response to s−i. b. Consider the same game in (a). If a IS NOT a best response to s−i, then a does NOT weakly dominates b. c. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, IS a best response to s−i, SO IS a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. d. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, is NOT a best response to some strategy profile of her opponents, s−i, NEITHER is a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. e. Consider the same game in (a). If a IS a best response to s−i, SO IS any mixed strategy that assigns positive probability to a. f. Consider the same game in (a). If a…
- 2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using. Maximax, maximin or minimax regret? Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using, the following decision criteria. Please explain your answer for each strategy. a)Maximax; b)Maximin; c)Minimax regret Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35
- . Ayça and Barış are playing a game and following payoff matrix is for the payoffs of Ayça. Answer the questions according to the following payoff matrix. a) What is the probability that the value of the game is 10?5 Historical data indicates that only 35% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 12 cable customers, what is the probability that between 3 and 5 (inclusive) customers are willing to switch companies? (Use TI 84 and round answer to at least 3 decimal places)A mutual fund company has 6 funds that invest in the U.S. market and 4 that invest in international markets. A customer wants to invest in two U.S. funds and 2 international funds.a. How many different sets of funds from this company could the investor choose?b. Unknown to this investor, one of the U.S. funds and one of the international funds will seriously underperform next year. If the investor selects funds for purchase at random, what is the probability that at least one of the chosen funds will seriously underperform next year?
- Given the following data with 25 % probability Bidder 1 bids 100 and Bidder 2 bids 80. What is the winning bid? Select the correct response 80 45 100 25In the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a.Twice in 5 hands. b. Ten or more times in 25 hands. Arrivals 0 1 2 3 4 5 6 7 8 Frequency 14 31 47 41 29 21 10 5 2Brown’s TV Production is considering producing a pilot for a comedy series for a major network. While the network may reject the pilot and series, it may also purchase the program for 1 or 2 years. Brown may produce the pilot or transfer the rights for the series to a competitor for $100,000. Brown’s profits are summarized in the following payoff table (profits in thousands). sate of nature reject 1 year 2 years produce pilot -100 50 150 sell to competitor 100 100 100 If the probability estimates for the states of nature are, P(reject)=0.20, P(1 year)=0.30, and P(2 years)=0.5, what is the maximum Brown should be willing to pay for inside information on what the network will do?