1. Consider the game with payoff matrix (0,0) (0, 2) (2, 0) (3, ) and let (–1, –1) be the NTU disagreement point. Find the corresponding agreement point based on the Nash bargaining that satisfies the Nash's bargaining axioms.
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- 26. An automobile dealer leases four types of vehicles: four-door sedans, sports cars, minivans, and sport utility vehicles. The term of the lease is 2 years. At the end of the term, customers must renoegotiate the lease and choose a new vehicle. Suppose that 80% of customers lease a vehicle of the same type at the end of each lease. However 10% of four-door sedan customers switch to sports cars, and 10% of sports car customers switch to four-door sedans. Similarly 10% of sport utility vehicle customers switch to minivans, while 10% of minivans customers switch to sports utility vehicles. The rest of the customers are 5% likely to switch vehicles as well. That means 5% of four-door sedan customers will switch to either a sports utility vehicle or a minivan 5% of sports car customers will switch to either a sports utility vehicle or a minivan 5% of minivan customers will switch to either a four-door sedan or a sports car, and • 5% of sports utility vehicle customers will switch to either…b) ABC company is engaged in manufacturing 5 brands of packet snacks. It is having five manufacturing setups, each capable of manufacturing any of its brands, one at a time. The cost to make a brand on these setups vary according to following table: B₁ B₂ B3 B4 B5 S₁ 4 7 8 9 7 S₂ 6 3 5 12 5 S3 7 6 4 7 9 5 9 6 11 8 S4 S5 11 5 9 10 11 Required Assuming five setups are S₁, S2, S3, S4, and S5 and five brands are B₁, B2, B3, B4, and B5, Find the optimum assignment of the products on these setups resulting in the minimum cost.
- The market of a cosmetic product is divided into two competitors, Alpha and Beta. Suppose that Beta has just entered the market and has 10% of the market shares, which means Alpha has the remaining 90%. Assume that every year, 26% of Alpha clients will switch to Beta, and that 14% of Beta clients will switch to Alphá. What will the market shares be in the long run? O a) Alpha: 55%, Beta: 45% O b) Alpha: 44%, Beta: 56% O c) None of these O d) Alpha: 45%, Beta: 65% O e) Alpha: 41%, Beta: 59% O f) Alpha: 37%, Beta: 63%2D1. A company is contemplating the introduction of a new product with new packing to replace the existing product at much higher Price (P) or a moderate change in the composition of the existing product with a new packaging at a small increase in price (P2) or a small change in the composition of the existing product except the word "new" with a very small increase in price (P3). The three possible states of nature are : (i) high increase in sales (n), (ii) no change in sales (n), and (iii) decrease in sales (na). The marketing department of the company calculated the payoffs in terms of yearly net profits from each of the strategies (expected sales). This is represented in the following table : Strategies States of Nature 3000 1500 PI P2 P3 7000 5000 3000 4500 3000 3000 Which strategy should the concerned executive choose on the basis of: (i) Maximin criterion, (ii) Laplace criterion ?
- The following table shows the stock market performance of 40 industries from five sectors of the U.S. economy in a certain year. (Take S to be the set of all 40 industries represented in the table.) Increased Decreased Unchanged (Z) Totals (X) (Y) Financials (F) 4 1 8. Manufacturing (M) 6. 4 4 14 Information 4 Technology (T) Health Care (H) 1 1 8. Utilities (U) 1 Totals 22 11 7 40 Use symbols to describe the event that an industry increased in value but was not in the manufacturing sector. OXn M' O X'U M' OX'n M OXUM X'n M' How many elements are in this event? 3.9. Consider a one-server queuing situation in which the arrival and service rates are given by n = 10-n, where n = 0,1,2,3, and n =+5, where n = 1,2,3,4. This situation is equivalent to reducing the arrival rate and increasing the service rate as the number in the system, n, increases. (a) Set up the transition diagram and determine the balance equation for the system. (b) Determine the steady-state probabilities.Flowering plant species can be subject to inbreeding, through self-fertilization. Some species have adaptations that help to avoid this inbreeding, through asymmetric flower structures. If the flower structures are “right-handed”, then a pollinator visiting the right-handed flower will get pollen on its left side, and thus, only be able to deposit the pollen on a left-handed flower that it visits later on. [Similarly, pollinator visits to left-handed plants will result in pollen deposits on right-handed plants.] You are interested in studying a particular plant species called Lupinus perennis, that demonstrates handedness, and you wish to know whether one type of handedness is more prevalent than the other (e.g., are left-handed plants more prevalent than right-handed plants?) You sample 30 L. perennis plants, and find that 20 plants are right-handed, and 10 plants are left-handed. Is one type of handedness more prevalent than the other? What is your null hypothesis? Report the…
- Banzhaf Power Index 1. Compute the Banzhaf power indices of players A, B, C, and D in the system [5 : 3,2,21] by determining the winning coalitions and the critical players.7.12) Thirty six percent of all assembly line mechanical robots are claimed for services by the technicians to be sent out to the manufacturer all under the issued warranty at the time of purchase. Out of these robots sent under warranty, 45% will be repaired and sent back to the factory and 55% will be replaced under warranty at no cost. Suppose the company you are working for recently ordered 15 of these mechanical robots. The CEO agreed to sign a five years purchasing contract if only the probability of sending back three of these robots are LESS than 0.24 during the life of the contract. Will she approve the purchasing contact? [Hint: you are trying to find the probability of exactly three robots will eventually be replaced under warranty as she will not sign off if such probability for three is more than 24%.]