4 Consider the multiround dictator game we looked at last class (see below),played 5 times in a row. What does the standard model predict will be eachplayer's payoff, summed over all 5 rounds?2550O 75Вoat 1SmallLargeSmall10,10 0,15Large15,05,5Suppose that, after each round, each person has a chance to take 5 pointsaway from the other person, if she chooses to do so. It costs the"punisher" 5 points to make the punishment. Based on the evidence welooked at in class, do you think overall payoffs will be:The same as without punishmentHigher than without punishmentO Lower than without punishmentO There is insufficient information to answer this questionBoat 2

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.5: Simulating Games Of Chance

Problem 36P: A martingale betting strategy works as follows. You begin with a certain amount of money and...

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You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.
Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poors 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another way to look at it that shows that Balboas beating the market 11 out of 13 times is not unusual. Consider 50 mutual funds, each of which has a 50% chance of beating the market during a given year. Use simulation to estimate the probability that over a 13-year period the best of the 50 mutual funds will beat the market for at least 11 out of 13 years. This probability turns out to exceed 40%, which means that the best mutual fund beating the market 11 out of 13 years is not an unusual occurrence after all.
Which of the following gambles has the largest objective risk? 20% chance of winning $100 and 80% chance of losing $100 50% chance of winning $10,000 and 50% chance of losing $10,000 50% chance of winning nothing and 50% chance of losing $100 50% chance of winning $100 and 50% chance of winning nothing
Player A and B play a game in which each has three coins, a 5p, 10p and a 20p. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, then A wins B’s coin. But, if the sum is even, then B wins A’s coin. Find the best strategy for each player and the values of the game.
Problem Solving. The JSM company has been approached by an individual who has an idea for a new product. He wants to sell this idea for P32, 000. If the idea is purchased, the product must be developed. The company can develop the product at a cost of P64,000, and there is a 50% chance that they can develop the product. TMJ INDUSTRY has offered to develop the product. It will also cost P65,000, but they are only 40% certain that they can develop the product. No charge will be levied unless the job is successful. If the product is developed, it must be advertised. There are two plans for the advertisement. Plan A which costs P55,000 with 75% chances of success and Plan B which cost P38,000 with a 50% probability of success. The management believes that if the product is a success, the return will be P50 million. a) Should JSM purchase the idea?b.) who should develop the product?c.) which plan of advertisement should be adopted?
At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…
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.
TenTen Company manufactures video recorders. It is so certain of its quality control that it is offering a complete replacement warranty if the set fails within two years. Based upon compiled data, the company has a need that only 1% of its recorders fail during the first year and 5% fail during the second year. The warranty does not cover replaced recorders. a) Formulate this problem as a Markov chain and determine the transition matrix. b) Find the probability that the manufacturer will have to honor the warranty.

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Consider the multiround dictator game we looked at last class (see below), played 5 times in a row. What does the standard model predict will be each player's payoff, summed over all 5 rounds? O 25 O 50 O 75