Consider the following Bargaining game, where each player tries to maximize his own number of coins. Player A starts the game with 3 coins and Player B starts with 1 coin. Player A needs to decide how many coins to give to Player B. Player A moves first, and makes an offer to Player B. Player B observes the offer, and then chooses to accept or reject the offer. If player B rejects the offer, the game is over: Player A loses all his 3 coins and player B losses his 1 coin (both players end up with zero coins). If Player B accepts the offer, the game is over: Player B keeps his original 1 coin plus the coin(s) offered by Player A, while Player A keeps the coin(s) he did not offer to player B. In the subgame perfect equilibrium of this game: Select the right option from below Player A offers zero coins to Player B Player A offers one coin to Player B Player A offers two coins to Player B Player A offers three coins to Player B Player A plays a mixed strategy

Consider the following Bargaining game, where each player tries to maximize his own number of coins. Player A starts the game with 3 coins and Player B starts with 1 coin. Player A needs to decide how many coins to give to Player B. Player A moves first, and makes an offer to Player B. Player B observes the offer, and then chooses to accept or reject the offer. If player B rejects the offer, the game is over: Player A loses all his 3 coins and player B losses his 1 coin (both players end up with zero coins). If Player B accepts the offer, the game is over: Player B keeps his original 1 coin plus the coin(s) offered by Player A, while Player A keeps the coin(s) he did not offer to player B. In the subgame perfect equilibrium of this game: Select the right option from below Player A offers zero coins to Player B Player A offers one coin to Player B Player A offers two coins to Player B Player A offers three coins to Player B Player A plays a mixed strategy

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 41P: Consider the following card game. The player and dealer each receive a card from a 52-card deck. At...

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In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
Suppose that two firms, an incumbent and a potential entrant, compete in a market. If they both operate, the resulting profits for the incumbent and the potential entrant are $30 million and $5 million, respectively. If the potential entrant decides not to enter the market, the resulting profits for the incumbent and potential entrant are $100 million and $0, respectively. Assume that it is not an option for the incumbent to exit the market. 1) Which of the two possible outcomes (for the potential entrant to enter or not enter) are Pareto efficient? 2) Now suppose there are side payments available. Which of the two possible outcomes is Pareto efficient? 3) Is it possible that the incumbent will agree to pay for the introduction of side payments? 4) Now suppose that side payments are allowed, but it costs $80 million in legal fees to actually use them. Which of the two possible outcomes (for the potential entrant to enter or not enter) are Pareto efficient allocations? (For simplicity,…
Consider the following game of ’divide the dollar.’ There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Draw the game tree.Consider the following variant of the ’divide the dollar’ game. Players 1 and 2 move simultaneously; 1 makes an offer to 2 and 2 specifies what would be an acceptable offer. For instance, player 1 might make an offer of 50 cents and player 2 might simultaneously set 25 cents as an acceptable offer. If player 1’s offer is at least as large as what is acceptable to player 2, then we will say that there is an agreement…
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.
Consider a cheap talk game in which Nature chooses the sender’s type andthere are three feasible types: x, y, and z, which occur with probability 1/4, 1/4,and 1/2, respectively. The sender learns her type and then chooses one of fourpossible messages: m1, m2, m3, or m4. The receiver observes the sender’smessage and chooses one of three actions: a, b, or c. The payoffs are shown in the table below. a. Suppose the sender’s strategy is as follows: (1) if the type is x, thenchoose message m1, and (2) if the type is y or z, then choose messagem2. The receiver’s strategy is the following: (1) if the message is m1,then choose action a; (2) if the message is m2, then choose action b;and (3) if the message is m3 or m4, then choose action a. For appropriatelyspecified beliefs for the receiver, show that this strategy pair is aperfect Bayes–Nash equilibrium.b. Find a separating perfect Bayes–Nash equilibrium.
Consider a firm run by an “incumbent” manager. Suppose the incumbent manager has the opportunity to invest in one of two different projects, Project 1 or Project 2. The incumbent manager has a higher ability in managing Project 1 rather than Project 2. Also, if theincumbent is fired by shareholders, she is replaced by an “alternative” manager whose ability to manage Project 1 is lower than the incumbent’s ability. Suppose the investment in a project is irreversible, and the shareholders’ choice of the incumbent manager salary (as well as their decision on whether to fire her) is taken afterthe investment is made. Also, assume the incumbent manager has a stake in the firm she runs, but she does not fully control it. Questions:(a) Suppose none of the projects gives the manager a direct utility. According to Shleifer and Vishny (1989), which of the two projects should the incumbent manager choose? What is the economic rationale behind this choice? Explain. (b) Suppose the incumbent…
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.
Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property, it can then be sold for $156,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $146,000. (a) What is the estimate of the probability Strassel will be able to obtain the property using a bid of $126,000? (Use at least 5,000 trials. Round your answer three decimal places.) (b) How much does Strassel need to bid to be assured of obtaining the property? $126,000 $136,000 $146,000 (c) Use the simulation model to compute the profit…
If a student attends every business analytics class, the probability of passing the course is 0.90; but if the student only attends randomly, then the probability of passing the course is 0.30. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.20 if the student has attended at random. Passing the course is worth 5 credits. Full-time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Draw a decision tree and use the decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the makeup exam and that the payoff for failing is equal to 0 credit. Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the student choose?
Problem 2: You go to the racetrack and are choosing between 2 horses: Belle and Jeb (you are at the racetrack, so you will bet on one of these two horses). Betting on either horse will cost you $1, and the payoffs are as follows: • Bet on Belle: you will be paid $2 if she wins (or a net profit of $1). You believe she has a 75% chance of winning. • Bet on Jeb: you will be paid $9 if he wins (for a net profit of $8). You believe that he has a 20% chance of winning. Prior to making your decision of which horse to bet on, someone comes and offers you gambler’s “insurance.” If you agree to the gamblers “insurance,” they pay you $1 immediately and you agree to pay them 50% of the profit on your winnings (that is, $0.50 if Belle wins, and $4 if Jeb wins). What should you do? Answer this question by: a) Creating a decision tree for this scenario, making sure you label all branches and include all probabilities and consequences. b) Solving the decision tree using EMV and stating the optimal…
Joe is a risk-averse decision maker. Which of thefollowing lotteries will he prefer?L1: With probability .10, Joe loses $100.L2: With probability .90, Joe receives $0.L2: With probability .10, Joe loses $190.L2: With probability .90, Joe receives $10.
Private Insurance provides coverages that can be used to meet specific loss situations. For each of the following insurance situation, identify a private insurance coverage that would provide the desired protection and explain your recommendation; A. John, 32, single parent with 1 dependent child. He recently purchased a house worth PhP 5 million, where half of this amount is mortgaged loan (PagIBIG). He wants to be certain that he would be able to pay his loan in case of disability. B. Rey, 36, married with 3 dependents. His wife is a disabled person and is unable to work. As the sole breadwinner, he wants to be sure that his family would have funds in case of his premature death. C. Marian, 44, owns a trading shop. The premises are rented. The total amount value of goods in her shop amounts to PhP 7 million. She has no savings. She wants to be certain she will be able to run her business if her shop catches fire and other loss. D. Dominic, 15, a talented motor racer. However, his…

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		Player A offers zero coins to Player B
		Player A offers one coin to Player B
		Player A offers two coins to Player B
		Player A offers three coins to Player B
		Player A plays a mixed strategy