In the following game, Player 1 makes a low bid or high bid, and Player 2 reacts in an easygoing or tough manner, resulting in the payoffs below. If the game is played twice, which actions occur in subgame perfect Nash equilibrium in both rounds? Player 2 Low (L) High (H) Easy (E) 5, 1 3, 3 Tough (T) -10, -10 -1, 1 Player 1 Low and Easy in both rounds. High and Easy in both rounds. Low and Easy in Round 1, High and Tough in Round 2. High and Easy in Round 1, Low and Tough in Round 2.
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- Suppose that you want to invest $10,000 in the stock market by buying shares in one of two companies: A and B. Shares in company A though risky, could yield a 50% return on investment during the next year. If the stock market if conditions are not favorable (bear market) the stock may lose 20% of it value. Company B provides safe investments with 15% return in a bull market and only 5% in a bear market Ali the applications you have consulted are predicting a 60% chance for a bull market and 40% for a bear market. Where you invest your money? Construct a decision tree.On Monday, a certain stock closed at $10 per share. Before the stock market opens on Tuesday, you expect the stock to close at $9, $10, or $11 per share, with respective probabilities 0.3, 0.3, and 0.4. Looking ahead to Wednesday, you expect the stock to close 10 percent lower, unchanged, or 10 percent higher than Tuesday’s close, with the following probabilities. Tuesday's Close 10 Percent Lower Unchanged 10 Percent Higher $9 0.4 0.3 0.3 10 0.2 0.2 0.6 11 0.1 0.2 0.7 Early on Tuesday, you are directed to buy 100 shares of the stock before Thursday. All purchases are made at the end of the day, at the known closing price for that day, so your only options are to buy at the end of Tuesday or at the end of Wednesday. You wish to determine the optimal strategy for whether to buy on Tuesday or defer the purchase until Wednesday, given the Tuesday closing price, to minimize the expected purchase price. Develop and evaluate a decision tree. a-1. Determine the optimal…A store owner must decide whether to build a small or a large facility at a new location. Demand at a location can be either small or large, which probabilities estimated to be 0.4 and 0.6, respectively. If small facility is built and demand proves to be high, the manager may choose not to expand (payoff=P235,000) or to expand (payoff=P275,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is P220,000. If a large facility is built and demand proves to be low, the choice is to do nothing (P60,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff grows to P230,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is P900,000.a.) Draw a decision tree.b.) Determine the expected payoff for each decision and event node.c.)…
- 1. If today stock is trading for $60 a share. You are confident that the stock price will experience a change in the value of over 30% relative to the current price in either upward or downward direction over the course of next year. Today you decide to transact in either one or two stocks maturing in one year. The strike price of both options is $60 a share. The call option premium is $6 and put option premium is $5. Given this information and your belief, you should _______. a. buy 2 calls b. buy 1 call and sell 1 put c. sell 1 call and 1 sell put d. buy 1 call and buy 1 put e. sell 2 puts Please explainSuppose that a sales force has found 20 qualified buyers and has begun the salesprocess. The sales manager estimates that 10% eventually proceeds to make a purchase.Assume that a professional company offers three services, priced at $2,000, $7,000 and$20,000, respectively. Based on past results or the sales manager’s estimates, you projectthat 60% of first-time buyers will choose the cheapest option, 30% will choose the middleoption and 10% will choose the most expensive option. a. Calculate the size of a likely sale for any prospect that makes a purchase.Martha and Ken Allen want to sell their house. At thebeginning of each day, they receive an offer. We assume thatfrom day to day, the sizes of the offers are independentrandom variables and that the probability that a given day’soffer is for j dollars is pj . An offer may be accepted duringthe day it is made or at any later date. For each day thehouse remains unsold, a maintenance cost of c dollars isincurred. The house must be sold within 30 days. Formulatea dynamic programming recursion that Martha and Ken canuse to maximize their expected net profit (selling price -maintenance cost). Assume that the maintenance cost for aday is incurred before the current day’s offer is received andthat each offer is for an integer number of dollars.
- An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits, in Kwacha, of each investment under each economic condition are indicated in the following payoff table: Event Investment selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: P (Economy declines) = 0.30 P (No Change) = 0.50 P (Economy expands) = 0.20 i. Compute the coefficient of variation for each investment. ii. Compute the return-to-risk ratio (RTRR) for each investment. iii. Based on (i) and (ii), what investment would you choose? Why?Consider the following information for the Alachua Retirement Fund, with a total investment of $4 million. [5] Stock Investment Beta A $ 400,000 1.2 B 600,000 -0.4 C 1,000,000 1.5 D 2,000,000 0.8 The market required rate of return is 12 percent, and the risk-free rate is 6 percent. What is its required rate of return? Stock A has the following probability distribution of expected returns: [5] Probability Rate of Return 0.1 -15% 0.2 0 0.4 5 0.2 10 25 What is Stock A’s coefficient of variation? What is Stock T’s coefficient of…Based on the following payoff table, answer the following: Alternative High Medium Low A 20 20 5 B 25 30 11 C 30 12 13 D 10 12 12 E 50 40 −28 Prior Probability 0.3 0.2 0.5 The Bayes’ decision rule strategy is: Multiple Choice: E. B. C. D. A.
- A retailer must decide whether to build a small or a large facility at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small facility is built and demand proves to be high, the manager may choose not to expand (payoff = $223,000) or to expand (payoff = $270,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is $200,000. If a large facility is built and demand proves to be low, the choice is to do nothing ($40,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff is estimated to be only $20,000; the payoff grows to $220,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is $800,000.Draw a decision tree. Then analyze it to determine the…In Benefit/cost ratio analysis, if the salvage value is used to recover the first cost, it is being considered as: Select one: a. negative cost b. cost c. benefit d. disbenefit =================== Ali takes out a loan at 10 percent compounded annually for 7 years. At the end of this period, he pays off the loan at a value of $23,384.61. What amount did he borrow? Select one: a. $12,000.00 b. $15,000.00 c. $14,000.00 d. $13,000.00 ============= While considering the engineering economy concepts, the most important tense almost all exercises deal with is the annual worth. Select one: True False Ans all1. George wishes to determine which of four investment strategies to use, given the payoff table here showing his annual returns (in thousands of shillings). The final outcome depends on what the government does in its upcoming tax bill. StrategyTaxes Go UpGo DownNo Change 1-255030 2-224030 3403550 4374050 a. Which investment strategy should James use if he is pessimistic regarding the future? b. Which investment strategy should James use of he is optimistic regarding the future? c. Which investment strategy should James use if he uses the Minimax Regret criterion? 2. Two different models are available for the same machine. The production statistics (number of units produced per hour) of these two models are given below. The data was collected on different days.Model A180176184181190137 Model B195194190192187185187 Will you conclude that Model A and Model B have the same productivity? 3. How large a sample should be selected to provide a 95% confidence interval with a margin of error…