Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the time while C uses the minimax strategy 50% of the time and chooses each of the other two columns 25% of the time. (Round your answer to two decimal places.)
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Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the time while C uses the minimax strategy 50% of the time and chooses each of the other two columns 25% of the time. (Round your answer to two decimal places.)
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- The payoff matrix for a game is −2 3 5 −2 1 1 1 −1 1 . (a) Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column player C uses the minimax pure strategy.(b) Find the expected payoff to the row player if R uses the maximin strategy 50% of the time and chooses each of the other two rows 25% of the time while C uses the minimax strategy 60% of the time and chooses each of the other two columns 20% of the time. (Round your answer to two decimal places.)An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?
- 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?In the Erlang loss model, system A has 5 servers and an implied utilization of 125 percent,while system B has 15 servers and an implied utilization of 125 percent. Which of thefollowing statements is true?a. System A has the higher utilization because it has fewer servers relative to the potentialdemand.b. The two systems have the same utilization because they have the same implied utilization.c. System B has a higher utilization because the fraction of lost demand is lower in that system.d. More information is needed to determine which system has the higher utilization.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.
- If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using MAXIMAX CRITERION? D1 D2 D3 D4 What decision alternative will he choose if using MAXIMIN CRITERION? D1 D2 D3 D4 What about MINIMAX REGRET CRITERION? D1 D2 D3 D4 What decision would he make if using criterion of realism at alpha 0.6 is used? D1 D2 D3 D4A 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?In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100.a. Write the above game in normal form. Player 1 Player 2 Strategy A B A $ , $ $ , $ B $ , $ $ , $ b. Find each player’s dominant strategy, if it exists.Player 1's dominant strategy: B no dominant strategy exists A .Player 2's dominant strategy: B no dominant strategy exists A .c. Find the Nash equilibrium of this game. (A,A) (B,A) (A,B) (B,B) d. Which strategy pair has the highest aggregate payoff? (B,A) (A,B) (B,B) (A,A) e. Can the outcome with the highest aggregate payoff be…
- A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with pmf x 1 2 3 4 5 6 p(x) 1/5 2/15 3/15 4/15 3/15 2/15 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00.If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the loadFind the saddle point of the game given by the payoff matrices A below.