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- Two travelers own an identical suitcase that contains identical antiques. The airline is liable for a maximum of $100 per suitcase. To determine how much to reimburse each traveler, the airline puts them in different rooms (so that they cannot communicate), and ask them to write down an amount (an integer number) between $2 and $100. If both write down the same number, the airline will reimburse both travelers that amount. However, if the two amounts are different, both travelers will be paid the lowest of the two numbers along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. What are the travelers’ best response functions? What are the Nash equilbria of the game? Are they Pareto efficient? Explain the intuition why.**Practice** In order to alleviate their risks, they are considering a risk-sharing agreement. Carol would buy one CC and David would buy one DD. Six months from now, they would sell their coins, add up the total amount of money, and split it equally between them. Thus, if only one of the coins is successful, they would both still have some positive amount of money at the end. Assume that they can verify whether the other really made the investment. They know whether the investment is successful, since the price of the coin is public information, and they trust that the other will pay them as promised. Which of the following statements is accurate?A. They will not make that risk-sharing agreement.B. Carol is willing to take the risk-sharing agreement, but David is not.C. They may be willing to make that risk-sharing agreement, but it depends on information not given in the question.D. They will surely make the risk-sharing agreement.E. None of the statements above is correct.Mete is Esra's boyfriend. Esra is expecting a marriage proposal from Mete. Today is Sunday. Mete says Esra that: (1) he is going to propose Esra on Monday or Tuesday or Wednesday or Thursday or Friday, at 10:00 pm. (2) he knows right now the day when he will propose (3) but the day of proposal will be a surprise to Esra: On the day of the proposal, she would not be expecting the proposal that day. Esra says Mete that what he says is impossible. Explain why Esra is right in a few sentences.
- In the late 1990s, car leasing was very popular In the United States. A customer would lease a car from the manufacturer for a set term, usually two years, and then have the option of keeping the car. If the customer decided to keep the car, the customer would pay a price to the manufacturer, the "residual value," computed as 60% Df the new car price. The manufacturer would then sell the retumed cars at auction. In 1999, manufacturers lost an average of $480 on each returned car (the auction price was, on average, $480 less than the residual value). Suppose two customers have leased cars from a manufacturer. Their lease agreements are up, and they are considering whether keep (and purchase at 60% of the new car price) their cars or return thelr cars. Two years ago, Becky leased a car valued new at $18,500. If she returns the car, the manufacturer could likely get $12,950 at auction for the car. Eleen also leased a car, valued new at $19,000, two years ago. If she returns the car, the…Nn3 Suppose an incumbent monopoly firm currently earns a profit of $50,000 per period. A potential entrant could enter and make a profit of $15,000 per period while also lowering the incumbent’s profit to $20,000 per period. The monopoly firm could seek to engage in predatory pricing, which would lead to both firms earning a loss of $5,000 per period. (a) Is there a Nash Equilibrium in this game? If so, what is it? (b) Discuss how this game might play out in the real world?Three players (player 1, player 2 and player 3) each chooses a positive integer QE {1, 2, 3, . 100}. If all three players choose the same integer Q, each player gets $100/3. If all three players choose different integers, the player with the largest integer gets $100, and the two other players get $0. If two players choose the same integer Q, and the third player chooses a different integer Q', then the player playing Q' gets $0, and the two players who played Q get $50 each. Find 2 Nash equilibriums in this game. ....
- DERIVATIVES Differentiate f(x)=(4x4+3x)(2x4+2x) Let u(x)=(4x4+3x) and v(x)=(2x4+2x)A class uses weighted averages to calculate your course grade. Homework, quizzes, and discussions are each worth 14% of your grade. A final exam is worth 40% and participation is worth 18%. A student has a score of 95 on homework, 89 on quizzes, 92 on discussions, 97 on participation, and earns 82 on their final exam. What is the weighted average of their course grade? Enter your answer as 1 decimal place.You work at a mechanic shop. 40% of cars that come in have a flat tire. If there are 50 cars in the shop, what is the probability that more than 30 have a flat tire? Round to three decimal points.
