Problem 3 Suppose you and your class mate have to do a group assignment. Both of you can decide to work or shirk. If you both work, then both will get a good mark but both incur the cost of working. If one person works, you get a bad mark but the person who shirked will not have to put in the effort. If both shirk then the students will get an even worse mark but do not have to put in effort. The following table represents the individuals' utilities (as always the first number is the payoff of the row player): you work shirk classmate work 4,4 5,1 shirk 1,5 2,2 e) Suppose both students are inequality averse and lose half a unit of utility for each unit difference in payoffs. In other words u(x, y) = x - - (ay)/2. Show the payoff table with the psychological payoffs. Find all pure-strategy Nash equilibria and discuss.
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- You like your job, but your boss gives lousy bonuses. You were recently offered a new job with better rewards and your friend wants to know if you intend to take it. You say, "It depends on whether the bonus this year is generous, Let's wait and see. We'll find out next week" The likely outcome of this game is your boss gives you a ousy :bonus and you ept the new job. If you want to stay at your current job and be better rewarded, you could improve your strategy if you: demand an increase in your bonus by a certain amount, but does not tel your boss about the job offer. adopt a dominant strategy to accept the other position and make this known to your boss. O tell the boss about the job offer you are prepared to take if your bonus structure does not increase by a certain amount. Cadopt a dominant strategy to stay at your current position and make this known to your boss.Problem 3 Suppose you and your class mate have to do a group assignment. Both of you can decide to work or shirk. If you both work, then both will get a good mark but both incur the cost of working. If one person works, you get a bad mark but the person who shirked will not have to put in the effort. If both shirk then the students will get an even worse mark but do not have to put in effort. The following table represents the individuals' utilities (as always the first number is the payoff of the row player): you work shirk classmate work 4.4 5,1 shirk 1,5 2,2 d) Suppose, both students have competitive preferences and care only about how much better or worse off they are compared to the other student. In other words, u(x, y) = IRI - y for both students. Show the payoff table with the psychological payoffs. What is the Nash prediction now! Discuss.2. Cindy and Andy are both workers on a team. At the same time both workers can choose to work on the risky project (R) or the safe project (S). If both choose to work on the R project the payoffs are 5 to Cindy and 4 to Andy. If both work on the S project the payoffs are 4 to Cindy and 5 to Andy. If Cindy works on R and Andy on S, the payoffs are (8, 10) to Cindy and Andy respectively. Finally, if Cindy plays S and Andy plays R, the payoffs are (10, 7). a. What are the Nash equilibria of the game? Interpret your equilibria in terms of a firm using teams. b. Now assume that Cindy can move first and choose which project to work on. Andy observes Cindy's choice before making his choice of either R or S. What are the subgame perfect equilibria of the game? Interpret this sequential game in terms of communication and leadership in organisations.
- Exercise 4.1 Amy and Bill simultaneously write a bid on a piece of paper. The bid can only be either 2 or 3. A referee then looks at the bids, announces the amount of the lowest bid (without revealing who submitted it) and invites Amy to either pass or double her initial bid. - The outcome is determined by comparing Amy's final bid to Bill's bid: if one is greater than the other then the higher bidder gets the object and pays his/her own bid; if they are equal then Bill gets the object and pays his bid. Represent this situation by means of two alternative extensive frames. Note: (1) when there are simultaneous moves we have a choice as to which player we select as moving first: the important thing is that the second player does not know what the first player did; (2) when representing, by means of information sets, what a player is uncertain about, we typically assume that a player is smart enough to deduce relevant information, even if that information is not explicitly given to…Two firms, A and B, are each considering trying to develop a newwidget. Whichever firm is first to develop the new widget wins a patent worth $20 million plus a penny.Developing a new widget involves several ‘steps’. The firms alternate moves, with A moving first, until oneof them wins the patent. All moves are observed. In each turn, a firm can choose whether to take 0, 1, or2 development ‘steps’. Taking 0 steps in a turn costs that firm $0. Taking 1 step in a turn costs $4 million.And taking 2 steps in a turn costs $11 million. For simplicity, assume a zero discount rate. Initially, eachfirm is 4 steps away from completing development.(a) Describe and explain carefully what will happen in this patent race and why. [Hint: it may help toread Dutta ch 12 (but notice I changed the numbers).](b) Very briefly explain what is the economic rationale for granting ‘intellectual property rights’ such aspatents. What are some disadvantages for society of granting such rights?In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F
- (1) Patricia owns a cleaning business with Sarah. They both have other jobs and are trying to determine the number of hours to work at the cleaning business. The following payoff matrix shows their daily incomes depending on the number of hours they work at the cleaning business. If Patricia chooses to work full time and Sarah works part time, what will each earn in daily income? A-Patricia will earn $60; Sarah will earn $60. B-Patricia will earn $50; Sarah will earn $80. C-Patricia will earn $80; Sarah will earn $50. D-Patricia will earn $55; Sarah will earn $55. E-Indeterminate (2) Company A and Company B are each telecommunications manufacturers. Both companies manufacture the same products, and they make their decisions based on the other's actions. Both companies are considering opening retail outlets to increase their profits. The payoff matrix shows the profits of the companies in millions of dollars if they choose to open retail outlets. The government imposes a new $5…Josiane and Nahed live in the beach town of batroun. They own a small business in which they make wristbands and pot holders and sell them to people on the beach. As shown in the table on the following page, josiane can make 30 wristbands per hour but only 6 pot holders. Nahed is a bit slower and can make only 24 wristbands or 4 pot holders in an hour. WRISTBANDS POT HOLDERS josiane 30 6 Nahed 24 4 a. For Josiane and for Nahed, what is the opportunity cost of a pot holder? Who has a comparative advantage in the production of pot holders? Explain your answer. b. Who has a comparative advantage in the production of wristbands? Explain your answer. c. Assume that Josiane works 20 hours per week in the business. Assuming Josiane is in business on her own, graph the possible combinations of pot holders and wristbands that she could produce in a week. Do the same for NahedWhile grading a final exam, an economics professordiscovers that two students have virtually identical answers.She is convinced the two cheated but cannot prove it. The professorspeaks with each student separately and offers the followingdeal: Sign a statement admitting to cheating. If both studentssign the statement, each will receive an “F” for the course. Ifonly one signs, he is allowed to withdraw from the course whilethe other student is expelled. If neither signs, both receive a “C”because the professor does not have sufficient evidence to provecheating.a. Draw the payoff matrix.b. Which outcome do you expect? Why?
- Mike and Tom debone chicken breasts for Ted's Chicken Co. Mike is new and can only debone 30 chicken breasts per hour by hand, while Tom's experience allows him to debone 60 chicken breasts per hour by hand. Ted buys one new machine that can debone 100 chicken breasts per hour. Both Mike and Tom work the same 40 hours per week, but one of them is assigned to operate the machine instead of deboning the chicken breasts by hand. To obtain maximum average hourly productivity, is assigned to use the machine and their combined average hourly productivity as a team is chicken breasts O a. Tom; 80 O b. Mike; 65 O c. Mike; 80 O d. Tom; 65Attempts 3. The relationship between marginal and average costs Consider the following scenario to understand the relationship between marginal and average values. Suppose Paolo is a professional basketball player, and his game log for free throws can be summarized in the following table. Fill in the columns with Paolo's free-throw percentage for each game and his overall free-throw average after each game. Game 1 2 3 Average / 4 4 LO 5 Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage 8/10 8/10 80 6/10 14/20 T 1/5 15/25 3/5 18/30 8/10 26/40 80Consider a repeated game with the following stage game: Player 1 O O O Cooperate Not Cooperate This game is repeated T-120 times, and t each period both players must choose their actions simultaneously. The players are deciding whether or not to cooperate specifically, whether or not to follow this cooperation strategy: r≤ 3 S|S|AW|N N|H "Each player will play cooperate as long as no one has played Not Cooperate before. If someone has played Not Cooperate before, then each player will play Not Cooperate forever." rs 5 rs Player 2 In this case, cooperation will be possible if the interest rate r is Not Cooperate 5,15 10, 10 None of the above Cooperate 12, 12 15,5