Unit 4 exercise answers - CORE · EXERCISE ANSWERS UNIT 4 Both these campaigns are examples of two-player games (Clinton v Trump, and Remain v Leave, respectively) where a similar

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EXERCISE ANSWERS UNIT 4

UNIT 4 ANSWERS TO EXERCISES

EXERCISE 4.1 SOCIAL DILEMMAS Using the news headlines from last week:

1. Identify two social dilemmas that have been reported (try to use examples not discussed above).

2. For each, specify how it satisfies the definition of a social dilemma.

Introduction This is an open-ended question that can be assigned before the lecture to see whether students understand the idea of a social dilemma, and also to underline how common they are in the world around us. Answer Here are two examples from recent headlines in the UK: Flooding in the north of England In December 2015 Storm Eva and Storm Frank caused devastating floods in cities across the north of England. Two major storm systems hit similar parts of England within the space of a week. This led to rivers bursting their banks and causing widespread flooding. Afterwards, questions were asked about the quality of flood defences and the amount of money which has been invested in them by the current government. Flood defences are a classic example of a social dilemma: when individuals act independently they are unlikely to take action to mitigate the effects of flooding. This is because no individual would be willing to finance the necessary investment. As a result, the government normally takes responsibility for providing the infrastructure. In this case the defences were ineffective. This may have been due to the severity of the storms (which might have been partly due to climate change, another social dilemma already discussed in U1), or perhaps to a lack of adequate investment. Air pollution in UK cities It was announced in early 2016 that it has taken some streets in London just eight days to break air pollution limits which are meant to cap emissions for the year. The EU has set limits on the hourly amount of nitrogen dioxide (NO2), a harmful gas produced by diesel vehicles, which can be produced per hour. Certain streets in London have breached this hourly limit more than ten times in the first quarter of 2016.

Parama Chaudhury

UNIVERSITY COLLEGE LONDON o Flooding in the north of England

(http://tinyco.re/6522353) o Air pollution in UK cities

(http://tinyco.re/7554554)

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Pollution is a classic example of a social dilemma as in a society where everyone acted in the own self-interest, they would pollute freely. This is because pollution is normally a by-product of a decision which leads to an economic benefit for the actor. Examples of this include pollution created in the production process, and people choosing the comfort of travel to work in a car rather than taking public transport. In the long run the economic benefits created as a by-product of air pollution do not outweigh the costs that it creates (in this case nitrogen dioxide has been shown to cause respiratory and heart problems). Because London has a large population, no individual can reduce his or her emissions by enough to have any impact on the level of air pollution, so there is little incentive to do it. A more desirable outcome could be reached if individuals came together and each agreed to limit their pollution to a non-harmful level. Marking guidance A good answer should:

• refer to the definition of a social dilemma • identify a social dilemma and be able to relate it to this definition

Teaching ideas If students find it hard to approach an open-ended assignment like this, the lecturer may start things off by showing students a collection of items from the news headlines and asking them to use the definition to identify which ones are social dilemmas and which ones are not. The lecturer might want to ask them to bring in a newspaper or magazine cutting (or e-version of the same) so that the discussion can focus on the specifics of each case. If there is a large class, the lecturer might want to divide students into small groups to go through each of the examples brought in, and compare them with the definition in the text. This question can also be brought back later in the unit, by asking students to model the social dilemma that they have found in the media. EXERCISE 4.2 POLITICAL ADVERTISING Many people consider political advertising (campaign advertisements) to be a classic example of a prisoners’ dilemma.

1. Using examples from a recent political campaign with which you are familiar, explain whether this is the case.

2. Write down an example payoff matrix for this case. Introduction The aim of this question is to help students apply the concept of a prisoner’s dilemma. Answer Consider the US presidential campaign and the UK referendum campaign about leaving the UE, both from 2016.

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Both these campaigns are examples of two-player games (Clinton v Trump, and Remain v Leave, respectively) where a similar outcome could have been achieved if both sides had agreed on lower spending on ads. So the cooperative outcome would have had higher payoffs (same outcome with lower costs), than the non-cooperative one. In the Nash equilibrium, both sides end up spending large amounts, as this is the dominant strategy. An example payoff matrix is given below, where the first entry is for Party A and the second for Party B. The payoffs here are defined as the value of winning the election, net of the cost of ad spending:

Party B spends Party B doesn’t spend

Party A spends 100, 100 250, 50

Party A doesn’t spend 50, 250 200, 200

Marking guidance A good answer:

• describes why political advertising is a prisoner’s dilemma • includes a payoff matrix as above (this does not need to be numerical) • uses a real life political campaign to explain

Teaching ideas Students should focus on a particular campaign (a municipal election, the independence vote in Scotland, and so on), and give examples of how the opposing parties used political advertising. It is obviously easier to make this connection if there are only two parties. If students can do some research on the amount of money spent on advertising, that would help put this discussion into perspective. The tricky bit is defining the benefit of advertising. This could be just the fact that it increases the probability that the party wins power, or that once it wins power, it makes it more likely that it can push its own political agenda, or that once in power, the party can line its own pockets more easily. Once these benefits and costs have been identified, students can write down a payoff matrix. Students could be asked to find estimates of how much the parties actually gained from spending. Public records often include spending accounts, and students will need to find out the percentage of votes or number of seats the parties gained. They will finally need to figure out a way to value these seats to come up with the final payoff matrix. Lecturers may want to refer to the article by David Vinjamuro on how political advertising has this structure.

o US presidential campaign 2016

(http://tinyco.re/8455671) o 2016 EU referendum campaign in the

UK (http://tinyco.re/3467500) o Vinjamuri, David, 2012. 'Political

Advertising Has Become A Prisoner's Dilemma'. Forbes, 10 April. (http://tinyco.re/5230735)

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EXERCISE 4.3 ALTRUISM AND SELFLESSNESS Using the same axes as in Figure 4.5:

1. What would Anil’s indifference curves look like if he cared just as much about Bala’s consumption as his own?

2. What would they look like if he derived utility only from the total of his and Bala’s consumption?

3. What would they look like if he derived utility only from Bala’s consumption?

For each of these cases, provide a real-world situation in which Anil might have these preferences, making sure to specify how Anil and Bala derive their payoffs. Introduction This is a straightforward question testing students’ ability to generate graphs from a description of preferences. There may be some discussion about the interpretation of these preferences. Answer

1. The first variation may generate some discussion about the interpretation of these preferences. One way to interpret this is that these preferences produce Leontief indifference curves (IC-A): Anil only gets utility when both he and Bala have higher payoffs. Another is that the ICs are the usual shape but symmetric around a 45-degree line from the origin (IC-B): a change in either one’s payoffs affects Anil’s utility in exactly the same way.

2. If he derived his utility from his and Bala’s TOTAL consumption then the indifference curves would be diagonal and linear (the exact same shape as the feasibility set). In the original graph, these indifference curves could be coincident with the feasible set (where 10 is divided between two players) as this line shows all the points where total consumption is equal to 10. The indifference curves would shift out as total consumption increased and shift closer to the origin as consumption decreases. IC-C in the graph above is an example of such indifference curves.

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3. If he only derived utility from Bala’s consumption, then the curves would be horizontal straight lines (IC-D in the graph above). This is because Anil now only values Bala’s consumption so will only be indifferent between points where Bala gets exactly the same amount regardless of the payoff that he receives. An intuitive way to think of this is to consider the shape of the curves when Anil was perfectly selfish. In this case we can think of him as being completely selfish on Bala’s behalf.

4. An example for the first set of preferences (IC-A) is if Anil and Bala each

own a firm that produces a different part of a product. For example, Anil owns a bicycle wheel factory and Bala owns a bicycle frame factory. Each person’s payoff depends on the number of completed units that he/she can produce, which in turn depends on how many parts the other person produces. Using the bicycle example, holding Bala’s production (and hence payoffs) constant, Anil’s payoffs do not increase if he makes more pairs of wheels than there are bicycle frames. An example for the second set of preferences might be if Bala is Anil’s spouse, so that his utility is based on household payoffs. The final set of preferences might result if Bala is Anil’s child, which might make him completely altruistic.

Marking guidance A good answer will:

• draw the graphs as above • explain how the preferences are depicted by the graph • be able to explain why Anil might have each of these preferences

Teaching ideas The examples above are extreme. The lecturer might want to suggest some real-life situations following on from the discussion in Q4. For example, how might Anil’s IC’s look if Bala was his child, or his partner, or his rival? Students may be asked to draw ICs relating their preferences and the ones of friends or family members to indicate how altruistic they feel. EXERCISE 4.4 AMORAL SELF-INTEREST Imagine a society in which everyone was entirely self-interested (cared only about his or her own wealth) and amoral (followed no ethical rules that would interfere with gaining that wealth). How would that society be different from the society you live in? Consider the following:

• families • workplaces • neighbourhoods • traffic • political activity (would people vote?)

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Introduction The focus here is on how much of what people do is because of altruism or ethical constraints, and how much is just a rational payoff-maximizing strategy. For example, families may care for children out of love or altruism, but this may also happen if caring for children is considered an investment, which may pay off in terms of future earnings some of which benefit the parents. Similarly, individuals may respect traffic laws for fear of punishment or because of a moral rule. Answer

• Families: The first and perhaps most drastic change that it is unlikely that anybody would have children. Raising children represents a significant financial burden, estimated to be in the hundreds of thousands of pounds, which is unlikely to be paid back, even in terms of support for elderly parents. It is unclear as to whether the institution of marriage would still exist. For many people marriage represents a significant cost (cost of a wedding, cost of taking time off work for a honeymoon, costs of spending time with spouse) and thus the amount of marriages may drop. Marriage may also generate cost savings, however (for example reducing the cost of housing and other services per person) and so, in some situations, marriage may represent a positive financial opportunity. For existing families (those who already have children) the home would become a place dominated by selfish acts. Jobs such as cleaning and cooking would not be done as no one would be willing to invest the time in an activity which benefitted the other members without financial reward. Parents who care for children would cease to provide this service and would instead focus on activities that increase their own payoffs.

• Workplaces: Workplaces will be dominated by selfish acts designed to increase the individual’s salary either through promotion or bonuses. Since workplaces are perhaps not dominated by altruism, this sphere may not be affected as much as others. Even if working in teams leads to greater group rewards, teamwork would be hard to facilitate. This is because employees will be constantly seeking opportunities to increase their reward by elevating their position in the team or forcing colleagues out in order to decrease the amount of reward which will be split. As a result, developing trust and delegating tasks will be extremely hard. Consequently, it is easy to conceive a world where everyone works alone.

• Neighbourhoods: The idea of ‘community spirit’ would disappear. Individuals would see no value in building friendships with neighbours unless they would lead to financial gain. As a result, neighbours would not do any favours for one another and volunteer groups such as the neighbourhood watch would not exist. Furthermore, the incidence of littering and other forms of non-altruistic behaviour would increase. This is because individuals are unlikely to care about anything other than their own gain so will see no value in creating a safe and tidy neighbourhood beyond their own homes, unless that affected their own outcomes (for example, their house price). Finally, crime would increase. In the absence of ethical rules, individuals who only cared about their own wealth would seek any opportunity to increase it and thus would take any opportunity to take wealth from another person. It is also likely that individuals prioritising their own financial gain would invest a lot of time/money

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in protecting their belongings from criminal activities. Gated communities and a rise in private security activities would be observed.

• Traffic: Road traffic is likely to be much less considerate. Acts such as letting other drivers through at junctions, and stopping to let pedestrians cross would be seen as a waste of time and thus would not occur. Furthermore, it would be much less safe. Drivers prioritizing only their own financial gain would place a higher value for getting to work on time so would be unlikely to stop for pedestrians or even observe road signs. This would dramatically increase the number of road accidents.

• Politics: Voting can be thought of as an altruistic task, as it involves taking the time to go to the polling station as well as any time spent researching the candidates, for no direct gain. Therefore, it is reasonable to expect that people prioritise going to work over voting and researching as the former activity leads to more financial gain than the latter activities. But, in a world where no one voted, a single person could decide the result by casting a vote in favour of the candidate who would benefit him/her the most. Therefore, as everyone will follow this logic everyone will want to vote for the candidate that benefits them the most. As a result, it is easy to see a world where everyone votes. In the case where everyone votes, it is easy to see how inequitable policies could be passed. For example, a politician who promised to take all of the income from 49% of people and give it to the other 51% will be elected. This is because 51% of people would see this policy as in their best interests and thus elect the politician.


• include a definition of what it means to be completely self-interested and amoral

• include specific examples from the contexts noted here

Teaching ideas As in each of these cases, the motivation may be either altruism, or the fear of punishment or stigmatisation, the lecturer may want to ask students to make this distinction in each of their examples, and whether their observations are more compatible with one motive or the other. For example, is the probability of being caught speeding high enough to prevent fast driving solely on the basis of fear of punishment?

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EXERCISE 4.5 ARE LAB EXPERIMENTS ALWAYS VALID? In 2007, Steven Levitt and John List published a paper called ‘What Do Laboratory Experiments Measuring Social Preferences Reveal about the Real World?’. Read the paper to answer these two questions.

1. According to their paper, why and how might people’s behaviour in real life vary from what has been observed in laboratory experiments?

2. Using the example of the public goods experiment in this section, explain why you might observe systematic differences between the observations recorded in Figures 4.9a and 4.9b, and what might happen in real life.

Introduction The focus of this question is on why experimental and observational data might differ. The reason is of course that humans may well behave differently under different conditions. Answer

1. Levitt and List identified five factors that could influence behaviour and lead to humans behaving differently in laboratory experiments compared to real life. These were:

• The presence of moral and ethical considerations and The nature and

extent of scrutiny of one's actions by others: The presence of researchers and other participants as well as the assumption that their actions will be made public may well lead people to act more altruistically than they otherwise would. This would be especially prevalent in an experiment designed to test how people behave in situations where no one is watching.

• The context in which the decision is embedded: It is very hard for people to state how they would behave in certain situations unless they are currently experiencing said situation themselves. Examples of this are situations where people are asked to state their actions under certain extreme circumstances as they may have little to no experience of making decision under these conditions.

• Self-selection of the individuals making the decisions: It seems likely that the people who willingly volunteer to take part in these experiments may exhibit similar behaviours. We can certainly state with confidence that they show a behavioural trait that enjoys taking part in experiments which may not be shared by the entire population. Participants in an experiment may also share non-behavioural characteristics, for example many experiments are conducted at universities where participants would likely be a similar age and have a similar level of education.

• The stakes of the game: In a laboratory, participants will be aware that any decision that they make will have no real-world consequences. Thus, there will be no rewards for a positive outcome or consequences for a negative outcome, aside from compensation for participating in the experiment. The paper also mentions that the differences in stakes matters and also depends on the setting of the game. Contributions decrease in a public goods experiment without punishment but are maintained when peer punishment is introduced. While it may be the

o Steven D. Levitt, and John A. List. 2007.

‘What Do Laboratory Experiments Measuring Social Preferences Reveal About the Real World?’ Journal of Economic Perspectives 21(2): pp. 153–174 (http://tinyco.re/9601240).

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case that peer punishment is the reason for sustained contributions, it is also possible that participants were responding to other aspects of the experiment. For example, the fact that they are being monitored, the size of the stakes, or a non-representative sample of participants.

2. What we expect to see in real life depends on how closely the situation resembles the conditions of the experiment. For example, there are situations in which it is much harder to identify and punish non-contributors, and we would expect public goods contribution to be lower than suggested in the experiment. In other situations that involve interactions with people we know e.g. villagers in a close-knit community, we would expect public goods contribution to be higher.


• identify the differences between a laboratory environment and real life. For example, subjects may have fewer distractions in a lab or they may behave differently when they are the subject of an experiment (so someone is watching). On the other hand, they could behave more altruistically in a real-life situation

• use the experiment referred to in the question to explain how the observational and experimental data would differ in this case

Teaching ideas Lecturers may want to encourage students to be as specific as possible in terms of their examples – does it matter what the experiment is, does it matter who the subject is, and so on? For the second question, students may want to think about whether the effect of having a punishment option might be quite as stark in real life (when you might already have some kind of social system that encourages altruism for example). Give students a list of questions and ask them which might be better answered using experiments and which ones using observational data. Is there a way to make this distinction systematically based on the question?

• Further reading: As an extension, field experiments can be contrasted with lab experiments. There are many papers on randomised controlled trials often in field experiments v observational data, for example here: http://tinyco.re/6493461.

EXERCISE 4.6 CROWDING OUT Imagine you are the mayor of a small town and wish to motivate your citizens to get involved in ‘City Beautiful Day’, in which people spend one day to help cleaning parks and roads. How would you design the day to motivate citizens to take part? Introduction This question gets at the heart of how to set up incentives in a situation with a potential for free-riding. Students may also have some experience of similar initiatives at universities or in their own towns, and therefore may have

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concrete ideas about how to design incentives. Answer The starting point for this answer is to define whom the mayor wants to target. Even if the target was 'all residents of the town', it is clear that different types of people will probably respond to different incentives. Some ideas for different incentives would be:

• Young people: Make the day something fun by having a live performance in parks during the clean-up drive.

• Families with children: Have face painting and other child-friendly activities along the roads/in the parks to attract children.

• Older people: If they are active, induce them to take part in the cleaning by inviting a celebrity from they know to accompany them. If they are unable to participate in the cleaning but looking for company, involve them in making tea for those cleaning, or doing shows for children while their parents clean.

A financial incentive would be the other obvious way to entice people to participate, but there is plenty of evidence that these do not work well in social activities (blood donation, or the day-care example in the textbook). There is also evidence that intrinsic motivation (social preferences) might work better than any kind of extrinsic motivation (market incentives), in which case the only incentive required might be a good marketing drive stressing how it is every citizen’s duty to clean up. Marking guidance A good answer will:

• distinguish between incentives for different sorts of people • discuss why monetary incentives may not work (or be too expensive) • explain why intrinsic motivation might work better than extrinsic

motivation

Teaching ideas Many students will have experience of something similar (a food bank or blood donation drive), so using these experiences in the class is a good idea. For example, the instructor could collect student experiences, form a list of possible incentives and then poll students on which of these incentives would get them to participate. Students can then discuss why they responded to certain incentives, think about how others (older people, those with kids, and so on) would respond, and make a list of incentives for different types of people.

o Gneezy, Uri, Stephan Meier, and Pedro

Rey-Biel, 2001. 'When and Why Incentives (Don’t) Work to Modify Behavior', Journal of Economic Perspectives, 25(4): pp. 191-210. (http://tinyco.re/2645111)

EXERCISE 4.7 ACCEPTABLE OFFERS

1. How might the minimum acceptable offer depend on the method by which the Proposer acquired the $100 (for example, did she find it on the street, win it in the lottery, receive it as an inheritance, and so on)?

2. Suppose that the fairness norm in this society is 50–50. Can you imagine anyone offering more than 50% in such a society? If so, why?

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Introduction This question aims to give students practice working out the rules in the Einstein. Answer There are some situations in which the proposer may offer more than 50% of the money to the responder:

• For altruistic reasons: The proposer may derive utility from the gains made by the partner and so will make a generous offer. An example: if family members played the game, many would offer over 50% to the other person due to altruistic preferences.

• For reasons based on how deserved it is: The proposer may feel that the responder has earned/deserves a greater split of the money as a result of its origins. For example, imagine that the proposer acquired the money through a project where the work was divided 75-25 in favour of the responder, as opposed to an equal split. In this scenario, the proposer would recognize that an offer of $75 may be fair.


• show their understanding of the algebra in the Einstein • offer realistic reasons for an offer over 50%

Teaching ideas The lecturer might want to give students some different scenarios for:

• how the $100 was obtained (paid as wages, a birthday gift, bank loan) • who the other player was (family member, friend, rival, stranger)

and ask them how R might change in each case. EXERCISE 4.8 SOCIAL PREFERENCES Consider the experiment described in Figure 4.12:

1. Which of the social preferences discussed above do you think motivated the subjects’ willingness to reject low offers, even though by doing so they would receive nothing at all?

2. Why do you think that the results differed between the Kenyan farmers and the US students?

3. What responses would you expect if you played this game with two different sets of players—your classmates and your family? Explain whether or not you expect the results to differ across these groups. If possible, play the game with your classmates and your family and comment on whether the results are consistent with your predictions.

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Introduction This question focuses on data from an actual experiment, and asks students to reflect on the background of the players, which might affect their behaviour. Answer

1. The most obvious answer here is that the subjects value fairness and a low offer violates their idea of fairness. The subjects show a preference towards punishing players who make an unfair or an unreasonable offer. We may say that they receive $x worth of satisfaction from rejecting what they deem to be an unreasonable offer and thus depriving their opponent of the money, where x is as least as high as the amount of money they are rejecting.

2. There could be many answers here including the fact that there are

cultural differences, and the Kenyan farmers may have more demanding norms of fairness than the US students. Students could either make a list of potential reasons, which the lecturer could then give feedback on based on the original paper (linked in the text). Or students could be asked to read the paper before making their list. It could be that Kenyan culture is more altruistic, and thus a social norm around sharing has developed. This would explain the farmers' unwillingness to accept low offers as they themselves would be unlikely to make such an offer if they were in that position, so they have higher expectations about what a fair offer is. The US students, on the other hand, may be more accepting of the pursuit of simple self-interest and would accept a lower offer as they would be likely to make a low offer if they were in that position.

3. When playing the game among family members we might expect an increased desire to be altruistic, which may result in a large number of 50-50 offers. This is due to individuals caring more about the family member than a stranger and thus having preferences which take their family’s wellbeing into account. When playing the game amongst classmates we might also expect a desire to be altruistic, but not as much as amongst family members. This is due to some classmates building relationships with each other but the bond not being as strong as amongst family members.


• be able to come up credible preferences to explain the results above • be able to predict the differences between playing the game with

family members, friends, and so on Teaching ideas For Q3, students may be divided into small groups to do this as a project over a couple of weeks. The lecturer may initially want to guide the students on how to choose the two sets of players. For example, they may choose other economics students v students in other fields. Or they may choose students v older people (university staff?). Ask them what differences they would predict, if any, and ask them to compare these predictions with the data once the project is completed.

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EXERCISE 4.9 OFFERS IN THE ULTIMATUM GAME

• Why do you think that some of the farmers offered more than 40%? Why did some of the students offer more than 30%?

• Why did some offer less than 40% (farmers) and 30% (students)?

• Which of the social preferences that you have studied might help to explain the results shown?

Introduction This is an extension of Exercise 4.7, Q1. It is important to make sure the students understand the significance of the ‘40%’ and the ‘30%’ in the question (these are the offers that maximize the expected payoff, as shown in the text). Answer

1. There are two possible reasons why participants may offer more than the amounts stated in the question:

• The individual may be altruistic and value the gains made by the

other. • The proposer feared a rejection and offered more to reduce the

likelihood of that occurring.

2. The answer to this question is the opposite of the two answers above. The individual may be more selfish and may place a higher value on his/her own consumption than the average participant in his/her group. Or, the player miscalculates the expected payoffs. More specifically, this means underestimating the minimum amount that the opponent would accept and making an offer that is too low. 1.

3. As discussed in the earlier answers, altruistic preferences may have influenced the amount offered. Inequality aversion may explain offers of a 50-50 split. Some of the offers may be motivated by fear of a rejection and hence, of receiving nothing.


• summarize the text explanation for the offers • suggest some insights into whether other social preferences might

also be relevant

Teaching ideas The discussion of why this might happen is mostly in the text immediately preceding the question. However, students may suggest other social preferences. In this case the lecturer may want to ask them to map these to the preferences mentioned in the text.

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EXERCISE 4.10 STRIKES AND THE ULTIMATUM GAME A strike over pay or working conditions may be considered an example of an ultimatum game.

1. To model a strike as an ultimatum game, who is the Proposer and who is the Responder?

2. Draw a game tree to represent the situation between these two parties.

3. Research a well-known strike and explain how it satisfies the definition of an ultimatum game.

4. In this section, you have been presented with experimental data on how people play the ultimatum game. How could you use this information to suggest what kind of situations might lead to a strike?

Introduction The main aim of this question is to test how well students can apply the concept of an ultimatum game. Answer

1. The proposer is the employer, and the responder is the employee or

union. 2.

2. The students should be able to produce a game tree looking like the diagram above.

3. There are many historical and contemporary examples of strikes.

4. From the UG, we see that people are often willing to reject what they consider to be an unfair offer even if it costs them a substantial amount of money much like the willingness of workers to reject an offer from their employer that they consider to be unfair going on strike and losing income as a result.


• identify a suitable example • draw the relevant game tree, like the one above

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• describe which data from UG experiments could be used to identify conditions under which strikes might occur

Teaching ideas The lecturer might ask students to bring to class a written account of the strike so that this can be used to answer the rest of the questions. For example, Collision Course is a well-known book about the air traffic controllers' strike in the US. In the UK, public transport, miners’ strike, or junior doctors’ strike are all straightforward to research. Students should be asked to identify the parties, and to draw the game tree, try to draw a timeline of events (and offers). This will also help answer the final question – using the timeline, students can write down a list of data required to test the predictions (the size of the offers, the consequent counteroffers or severity of strike action). Students will need to ascertain whether after the employer’s opening offer, there was a possibility for workers to make a counteroffer (in which case the game is more complicated than an ultimatum game), or the only options are to accept or reject the offer.

• Extension: Look at two strikes, one with the employers triumphing at the end, and the other with the employees having the last laugh. Discuss why these two games had different outcomes.

o McCartin, Joseph A, 2011. Collision

Course, Ronald Reagan, the Air Traffic Controllers, and the Strike that Changed America. Oxford: Oxford University Press.

EXERCISE 4.11 A SEQUENTIAL PRISONERS’ DILEMMA Return to the prisoners’ dilemma pest control game that Anil and Bala played in Figure 4.3b, but now suppose that the game is played sequentially, like the ultimatum game. One player (chosen randomly) chooses a strategy first (the first mover), and then the second moves (the second mover).

1. Suppose you are the first mover and you know that the second mover has strong reciprocal preferences, meaning the second mover will act kindly towards someone who upholds social norms not to pollute and will act unkindly to someone who violates the norm. What would you do?

2. Suppose the reciprocal person is now the first mover interacting with the person she knows to be entirely self-interested. What do you think would be the outcome of the game?

Introduction The aim of this question is to test students’ understanding of the prisoners’ dilemma and the importance of how small changes in the rules of the game – it being played sequentially and the introduction of social preferences – can fundamentally change the outcomes.

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Answer

1. If the responder is highly reciprocal, then she will do whatever the first mover does. She will respect the social norm if the first mover respects it, and will violate the norm if the first mover violates it. In this situation, you can see from the payoff table that there are just two outcomes: both use IPC and receive 3, or both use Terminator and receive 2. The first mover is faced with the choice between only they possible outcomes and so will choose IPC.

2. Knowing that the second mover is entirely selfish, the first mover as a reciprocator will adopt Terminator as the dominant strategy, to which the second mover will respond with Terminator, giving each a payoff of 2.


• show a good answer of the prisoner’s dilemma • show how playing the game sequentially may lead to the Pareto-

efficient outcome

Teaching ideas Divide students into groups and ask one group what the second mover would do, then ask the other group what the first mover would do. EXERCISE 4.12 CONFLICT BETWEEN ASTRID AND BETTINA What is the likely result of the game in Figure 4.16b if:

1. Astrid can choose which language she will use first, and commit to it (just as the Proposer in the ultimatum game commits to an offer, before the Responder responds)?

2. The two can make an agreement, including which language they use, and how much cash can be transferred from one to the other?

3. They have been working together for many years, and in the past they used Java on joint projects?

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Introduction This question is a chance for students to think a bit more about the coordination game, as we will use this game again when we discuss public goods in Unit 11 and innovation in U21. Answer

1. She will choose Java as it gives her the highest payoff ($4,000). Bettina will then choose Java because it gives her a payoff of $3,000 compared to $2,000 from C++, resulting in payoffs of ($4,000, $3,000).

2. They will both choose C++ and Bettina will transfer $1,000 (or a little

bit more) to Astrid to give her the highest possible payoff she can attain (a little bit more than $4,000). Bettina is also better off even after making the payment, as she receives $5,000 (or a little less), which is more than her payoff from (Java, Java).

3. In this case, we have to take into account the costs of learning the new

language C++ and any other setup costs. If they change to C++, their total payoffs rise to $9,000 (from $7,000 when both are using Java), which can be redistributed as above to sustain this equilibrium. This means that if the cost of switching to C++ is larger than $1,000 per person ($9,000 - $7,000 - $1,000), the switch is not profitable.


• provide the numerical justifications for the first two questions • recognize the setup costs involved in the third question

Teaching ideas This question might be paired with the next question to show students how this situation might turn out in real life. EXERCISE 4.13 CONFLICT IN BUSINESS In the 1990s, Microsoft battled Netscape over market share for their web browsers, called Internet Explorer and Navigator. In the 2000s, Google and Yahoo fought over which company’s search engine would be more popular. In the entertainment industry, a battle called the ‘format wars’ played out between Blu-Ray and HD-DVD. Use one of these examples to analyse whether there are multiple equilibria and, if so, why one equilibrium might emerge in preference to the others. Introduction The aim of this question to test how well students can apply their knowledge of the coordination game. This problem is dealt with explicitly in Unit 21.

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Answer Example: Blu-Ray v HD-DVD Between 2000 and 2003, both Sony (Blu-Ray) and Toshiba (HD-DVD) began to develop technology to offer consumers high definition DVDs. As they were developed independently, the two formats were not compatible (Blu-Ray DVD’s could not be played on HD-DVD players, and vice versa). In 2004 talks to merge the two formats broke down, leading to what was known as the ‘format war’. Thus, between 2005 and 2008 both firms competed to establish dominance in the market. They did this through advertising that their own format was superior and by signing exclusive deals with film production companies. Each firm has 2 options, to produce or not to produce. If both firms produce both will make losses. If only one firm produces, it becomes a monopolist and makes profits. If neither firm produces they both break even. This means there are two equilibria:

In this case, if one of the technologies was superior to the other, the payoff matrix would look like this:

Eventually in 2008 one equilibrium did emerge. Blu-ray became the clear winner and Toshiba stopped manufacturing HD-DVD players. This was because:

• Sony offered Blu-ray as standard for its PS3 console, meaning that consumers had to purchase Blu-Ray DVDs to watch content on their devices.

• Film production companies favoured Blu-ray. Marking guidance A good answer will:

• link to a reliable source on their chosen game • be able to analyse the game using the language in the text

Teaching ideas Divide the class into three groups, and ask each group to research one of these games. Each group should analyse its assigned game, draw a payoff matrix or game tree if possible, and identify any equilibria. Then each group can present their work to the others. The groups should also research how these games were resolved, if at all.

o Kiss, Jemima, 2008. 'Sony's Blu-Ray

wins HD DVD battle'. The Guardian, 19 February. (http://tinyco.re/6221024)

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EXERCISE 4.14 NASH EQUILIBRIA AND CLIMATE CHANGE Think of the problem of climate change as a game between two countries called China and the US, considered as if each were a single individual. Each country has two possible strategies for addressing global carbon emissions: Restrict (taking measures to reduce emissions, for example by taxing the use of fossil fuels) and BAU (the Stern report’s business as usual scenario). Figure 4.17 describes the outcomes (top) and hypothetical payoffs (bottom), on a scale from best, through good and bad, to worst. This is called an ordinal scale (because all that matters is the order: whether one outcome is better than the other, and not by how much it is better).

1. Show that both countries have a dominant strategy. What is the dominant strategy equilibrium?

2. The outcome would be better for both countries if they could negotiate a binding treaty to restrict emissions. Why might it be difficult to achieve this?

3. Explain how the payoffs in the bottom right of Figure 4.17 could represent the situation if both countries were inequality averse and motivated by reciprocity. Show that there are two Nash equilibria. Would it be easier to negotiate a treaty in this case?

4. Describe the changes in preferences or in some other aspect of the problem that would convert the game to one in which (like the invisible hand game) both countries choosing Restrict is a dominant strategy equilibrium.

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Introduction The focus of this question is to test understanding of the coordination game. Answer

1. First, consider China. If the US chooses Restrict, China’s best response is BAU. If the US chooses BAU, China’s best response is BAU. Hence China’s dominant strategy is BAU. Next, consider the US. If China chooses Restrict, the US best response is BAU. Likewise, the US best response is BAU if China chooses BAU. Hence the US dominant strategy is also BAU. If both countries play their dominant strategy, the dominant strategy equilibrium is (BAU, BAU).

2. (Restrict, Restrict) is not a Nash equilibrium, because each country can

benefit from deviating. The country that deviates to BAU will be better off (receiving the ‘best’ payoff rather than just a ‘good’ payoff), while the other country receives the ‘worst’ payoff. This beneficial deviation makes it difficult for countries to commit to (Restrict, Restrict), even if they could reach an agreement.

3. If countries were inequality averse, then they would prefer outcomes

where both countries receive the same payoffs: (Restrict, Restrict) or (BAU, BAU). If they were also motivated by reciprocity then they might be willing to restrict emissions, as long as the other country did the same. Hence, the payoff matrix may look like Figure 4.18b, with two Nash equilibria. Note that BAU is still a Nash equilibrium, but is no longer a dominant strategy equilibrium.

4. For (Restrict, Restrict) to be the only dominant strategy equilibrium, the game would need to be adapted so that the payoffs for playing Restrict were higher, regardless of the opponent's strategy. An example of a preference change leading to this equilibrium would be an emissions trading scheme in which countries were rewarded for restricting emissions and punished for polluting, thus increasing their payoffs when they play Restrict. Alternatively, a restriction could be placed on the game, such as a treaty preventing either county from playing BAU, eliminating it as an option (as discussed). This can also be the case if, for example, business as usual is now considered to be selfish and countries get disutility from being considered selfish. Reducing the benefits of BAU or increasing those of Restrict might do this as well. This could easily happen, for example, if the price of solar panels maintains its recent rate of decrease.


• recognize the difference in incentives required for the symmetric and asymmetric equilibria

• give concrete examples of preferences, technology or institutions that may give rise to each of these equilibria

Teaching ideas Students may be asked to research the recent history of climate change agreements and why they are difficult to sustain. This is discussed further in Unit 20.

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Unit 4 exercise answers - CORE · EXERCISE ANSWERS UNIT 4 Both these campaigns are examples of two-player games (Clinton v Trump, and Remain v Leave, respectively) where a similar