Tag Archives: economic theory

Self-balancing computer game

In both tabletop role-playing and computer games where players choose between different characters, some characters may be stronger than others when played optimally. This is undesirable in multiplayer games, because either most players will choose the stronger characters or some players will be handicapped by their weak character, which tends to reduce the enjoyment. Game designers spend time and resources “balancing” the game, i.e. changing aspects of the characters to give them all approximately equal strength. It is difficult to predict all possible ways a character may be played, so players may discover tricks that make a character significantly stronger than others. To counteract this, the game can be made self-balancing: the more players choose a given character, the weaker that character becomes. Then the discovery of ways to play a character better (giving additional strength) initially benefits the discoverer, but is neutralised with widespread imitation, analogously to innovative firms reaping monopoly profits initially from their patents, but eventually losing their competitive advantage to imitators.
The simplest way to self-balance is to subtract some measure of strength, e.g. health points, armor, attack points from the most frequently chosen characters. One in-game interpretation of this loss of strength to crowding is that each character channels power from some source (magic item, god, nature) and if more people channel a given source, then each of them gets less power. There are other ways to impose a negative congestion externality to achieve self-balancing.
One source of congestion-induced weakening is that in-game enemies (NPCs) fight better against characters they frequently encounter. This can be interpreted as learning (if the enemies flee before dying and later come back) or evolution (if the longer-surviving enemies multiply relatively more). In an evolutionary arms race, players pick characters that are strong against frequently encountered NPCs. NPCs vary in their resistance to different attacks and relatively more copies are spawned of those who last the longest under player attack.
Another congestion externality is a shortage of some resource that strengthens a particular class of characters. For example, equipment usable by that class may be in limited supply, in which case if many players choose that class, then they will find themselves under-equipped and weak. There could also be a shortage of materials for manufacturing the equipment, or a shortage of class-specific quests for gaining experience.
To make players (as opposed to NPCs or the game mechanics) the source of disadvantage to a frequently chosen class, the classes should have advantages over each other in a cycle, for example archers defeat riders, riders defeat swordfighters, swords defeat archers. In this case, if a class is frequently chosen, then this invites other players to choose another class that has an advantage over the frequent class, e.g. if many have chosen riders, then this creates an incentive to choose archers. Such a cyclical evolutionary dynamic has been observed in lizards (Rapid Temporal Reversal in Predator-Driven Natural Selection, Science 17 Nov 2006 Vol. 314, Issue 5802, pp. 1111).

Signs with strong language are not enforced

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Various prohibiting signs are posted in many places, saying for example “No smoking”, “No trespassing”, “No skateboarding”, etc. The language of a sign with the same message can be stronger or weaker, e.g. “Smoking prohibited” vs “No smoking. Strictly enforced” or “Trespassing forbidden” vs “Strictly no trespassing. Violators will be prosecuted to the fullest extent of the law.” It seems that there is a negative correlation between the strength of the language and the strength of enforcement. The rules stated on signs threatening strict enforcement or prosecution seem not enforced at all. Non-enforcement is certainly the case for the “Smoke-free campus. Strictly no smoking” signs around the Australian National University and for similar signs around other universities that I have visited.
Why might stronger language of the sign indicate non-enforcement? Stronger language is also longer, requiring a larger sign and more paint, which makes signs with stronger language slightly more expensive to put up. So why pay more for signs that suggest non-enforcement?
Local people learn the rules and their actual level of enforcement over time. For them, signs are not really necessary. Therefore, signs are put up only for first-time visitors or for legal reasons. Legalities usually just require some legible sign, not a long and strongly worded one, so to satisfy the law, the optimal choice is a shorter and simpler text that fits on a smaller, cheaper sign.
First-time visitors are either uncertain about the enforcement level or know it. If they know, then they are effectively locals – for them, there is no need for a long sign. If the visitors are uncertain, then they might infer the enforcement level from the strength of the language. This can go two ways. If the visitors are rational and the strength of the language is negatively correlated with the level of enforcement, then a shorter sign signals stronger enforcement and deters rule-breaking better. Then all signs would optimally be short. If the visitors are irrational and interpret the signs literally, then more strongly worded signs deter rule-breaking more. The negative correlation between strong language and enforcement suggests that people are irrational and take threats literally. Or that those putting up signs are irrational and for some reason choose the less effective strongly worded signs.
An alternative explanation is countersignalling (Feltovich, Harbaugh and To 2002). In this model, there are three types of sign-posters. The first type does not care much about whether the text of the sign is obeyed (may post the sign only for legal reasons). The second type cares a little bit, but not enough to pay for much enforcement. Still, the second type slightly enforces, so there is a small positive probability of some kind of punishment when breaking the rules. The third type really wants the rules to be followed and invests in enforcement correspondingly. The potential rule-breakers quickly learn from punishments whether they are dealing with the third type. So the third type does not need any particular kind of signs to distinguish himself from the first two.
The first two types are harder to tell apart. The first type is not interested in distinguishing himself from the others – in fact, being confused with the others is beneficial, because it is more likely to make people obey the rules. The second type would like to distinguish himself from the first type and be confused with the third type, but this desire is not strong enough to pay the same enforcement cost as the third. So the second type will settle for distinguishing himself from the first type. This is done by paying for slightly larger signs with stronger, longer language on them. In this case, in the absence of experienced enforcement, the potential rule-breakers respond more to strongly worded signs than to short ones.
For an external observer, it is difficult to distinguish a small amount of enforcement from none, so the perception arises that enforcement goes together with short signs, but non-enforcement sometimes with long, strongly worded signs and sometimes with short signs. So there is a negative correlation between the strength of enforcement and the strength of the language. This correlation is stronger if the fraction of the first type in the population of sign-posters is small, for example because some first types do not post signs at all. People posting signs are a selected sample from the population of those who want some rule obeyed. The selection oversamples those who care more.

“Relative to opportunity” evaluation and anti-discrimination laws

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Most countries have some anti-discrimination laws, requiring employers to pay people with different productivities equally, or to give someone who took parental leave their job back after they return. One reason why unequally productive people are paid equally is evaluation “relative to opportunity”, i.e. the bar for a promotion or a raise is lower for someone from a historically disadvantaged group or who has family responsibilities. Suppose that there is a consensus in society for supporting certain groups. Why might the cost of this support be placed only on specific employers, namely those who employ the target group? Why doesn’t the support take the form of direct subsidies from the government to the target group, financed by taxing all employers equally?
An explanation from political economy is as follows. Clever people in society or government want to pay a larger subsidy to high-income members of the target group, perhaps because the clever people are themselves high-income and belong to the target group. However, the majority of voters would not like high-income people getting a bigger subsidy. So the clever people disguise the subsidy as something that looks equal, namely every member of the target group gets the same duration of parental leave, the same guarantee of their job back at the end of leave, the same privileges and special treatment for promotions and raises. The value of these guarantees and privileges is greater for higher-paying jobs. For example, a promotion from a high-paying job usually gives a bigger salary increase than from a low-paying job. A guarantee of getting a high-paying job back after parental leave is worth more than a guaranteed low-paid job. Thus the support provided to the high-income members of the target group is more valuable.
Further, productivity at a high-income job is typically more responsive to the employee’s human capital, and the skills deteriorate faster. A truck driver who has not driven for some years retains a greater fraction of driving ability than a surgeon retains from surgical technique after not operating for the same number of years. The productivity difference between an employee returning from parental leave and someone continuously employed is on average greater for higher-paying jobs. So the cost to an employer of keeping a job for a returning employee instead of hiring a new person is greater if the job is higher-paid. The subsidy to the high-income members of the target group thus costs more per person.
Income is positively correlated with intelligence, so the smart members of the target group are likely the wealthy members who benefit from this kind of unequal subsidy. They are likely to vote and campaign in favour of the unequal support, instead of an equal cash subsidy for everyone. The less smart members of the target group who lose from an unequal subsidy (compared to an equal one) are less likely to understand that they lose. This makes them abstain from opposing the unequal subsidy.
In effect, the smart members of the target group redistribute a baseline-equal subsidy from the less smart (and less wealthy) to themselves, at the social cost of losing some efficiency in the economy. Keeping a job for someone when a more productive potential hire is available means losing the difference in the productivities of the two people. Such efficiency losses are typical of re-distributive policies that are not cash transfers.
In principle, the cost of the current policies could still be equally distributed between employers by taxing them all and subsidising those who employ the target group. Or equivalently, taxing only those who don’t employ the target group. However, to equalise the cost to employers, the firms employing highly-paid members of the target group must be compensated more than the ones employing low-paid members. The differential compensation to firms would call attention to the unequal support that people with different incomes are receiving, thus weakening the disguise of the subsidy. The clever people want to avoid that, so do not campaign for equalising the costs of anti-discrimination laws across employers.

Defence against bullying

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Humans are social animals. For evolutionary reasons, they feel bad when their social group excludes, bullies or opposes them. Physical bullying and theft or vandalism of possessions have real consequences and cannot be countered purely in the mind. However, the real consequences are usually provable to the authorities, which makes it easier to punish the bullies and demand compensation. Psychological reasons may prevent the victim from asking the authorities to help. Verbal bullying has an effect only via psychology, because vibrations of air from the larynx or written symbols cannot hurt a human physically.

One psychological defense is diversification of group memberships. The goal is to prevent exclusion from most of one’s social network. If a person belongs to only one group in society, then losing the support of its members feels very significant. Being part of many circles means that exclusion from one group can be immediately compensated by spending more time in others.

Bullies instinctively understand that their victims can strengthen themselves by diversifying their connections, so bullies try to cut a victim’s other social ties. The beaters of family members forbid their family from having other friends or going to social events. School bullies mock a victim’s friends to drive them away and weaken the victim’s connection to them. Dictators create paranoia against foreigners, accusing them of spying and sabotage.

When a person has already been excluded from most of their social network, joining new groups or lobbying for readmission to old ones may be hard. People prefer to interact with those who display positive emotions. The negative emotions caused by a feeling of abandonment make it difficult to present a happy and fun image to others. Also, if the „admission committee” knows that a candidate to join their group has no other options, then they are likely to be more demanding, in terms of requiring favours or conformity to the group norms. Bargaining power depends on what each side gets when the negotiations break down – the better the outside option, the stronger the bargaining position. It is thus helpful to prepare for potential future exclusion in advance by joining many groups. Diversifying one’s memberships before the alternative groups become necessary is insurance. One should keep one’s options open, which argues for living in a bigger city, exploring different cultures both online and the real world, and not burning bridges with people who at some point excluded or otherwise acted against one.

There may be a case for forgiving bullies if they take enough nice actions to compensate. Apologetic words alone do not cancel actions, as discussed elsewhere (http://sanderheinsalu.com/ajaveeb/?p=556). Forgiving does not mean forgetting, because past behaviour is informative about future actions, and social interactions are a dynamic game. The entire sharing economy (carsharing, home-renting) is made possible by having people’s reputations follow them even if they try to escape the consequences of their past deeds. The difficulty of evading consequences motivates better behaviour. The same holds in social interactions. In the long run, it is better for everyone, except perhaps the worst people, if past deeds are rewarded or punished as they deserve. If bullying is not punished, then the perpetrators learn this and intensify their oppression in the future.

Of course, the bullies may try to punish those who reported them to the authorities. The threat to retaliate against whistleblowers shows fear of punishment, because people who do not care about the consequences would not bother threatening. The whistleblower can in turn threaten the bullies with reporting to the authorities if the bullies punish the original whistleblowing. The bullies can threaten to punish this second report, and the whistleblower threaten to punish the bullies’ second retaliation, etc. The bullying and reporting is a repeated interaction and has multiple equilibria. One equilibrium is that the bullies rule, therefore nobody dares to report them, and due to not being reported, they continue to rule. Another equilibrium is that any bullying is swiftly reported and punished, so the bullies do not even dare to start the bullying-reporting-retaliation cycle. The bullies rationally try to push the interaction towards the equilibrium where they rule. Victims and goodhearted bystanders should realise this and work towards the other equilibrium by immediately reporting any bullying against anyone, not just oneself.

To prevent insults from creating negative emotions, one should remember that the opinion of only a few other people at one point in time contains little information. Feedback is useful for improving oneself, and insults are a kind of feedback, but a more accurate measure of one’s capabilities is usually available. This takes the form of numerical performance indicators at work, studies, sports and various other tests in life. If people’s opinions are taken as feedback, then one should endeavour to survey a statistically meaningful sample of these opinions. The sample should be large and representative of society – the people surveyed should belong to many different groups.

If some people repeatedly insult one, then one should remember that the meaning of sounds or symbols that people produce (called language) is a social norm. If the society agrees on a different meaning for a given sound, then that sound starts to mean what the people agreed. Meaning is endogenous – it depends on how people choose to use language. On an individual level, if a person consistently mispronounces a word, then others learn what that unusual sound from that person means. Small groups can form their own slang, using words to denote meanings differently from the rest of society. Applying this insight to bullying, if others frequently use an insulting word to refer to a person, then that word starts to mean that person, not the negative thing that it originally meant. So one should not interpret an insulting word in a way that makes one feel bad. The actual meaning is neutral, just the „name” of a particular individual in the subgroup of bullies. Of course, in future interactions one should not forget the insulters’ attempt to make one feel bad.

To learn the real meaning of a word, as used by a specific person, one should Bayes update based on the connection of that person’s words and actions. This also helps in understanding politics. If transfers from the rich to the poor are called „help to the needy” by one party and „welfare” by another, then these phrases by the respective parties should be interpreted as „transfers from the rich to the poor”. If a politician frequently says the opposite of the truth, then his or her statements should be flipped (negation inserted) to derive their real meaning. Bayesian updating also explains why verbal apologies are usually nothing compared to actions.

Practicing acting in a drama club helps to understand that words often do not have content. Their effect is just in people’s minds. Mock confrontations in a play will train a person to handle real disputes.

Learning takes time and practice, including learning how to defend against bullying and ignore insults. Successfully resisting will train one to resist better. Dealing with adversity is sometimes called „building character”. To deliberately train oneself to ignore insults, one may organise an insult competition – if the insulted person reacts emotionally, then the insulter wins, otherwise the insulter loses. As with any training and competition, the difficulty level should be adjusted for ability and experience.

The current trend towards protecting children from even verbal bullying, and preventing undergraduate students from hearing statements that may distress them could backfire. If they are not trained to resist bullying and experience it at some point in their life, which seems likely, then they may be depressed for a long time or overreact to trivial insults. The analogy is living in an environment with too few microbes, which does not build immunity and causes allergy. „Safe spaces” and using only mild words are like disinfecting everything.

The bullies themselves are human, thus social animals, and feel negative emotions when excluded or ignored. If there are many victims and few bullies, then the victims should band together and exclude the bullies in turn. One force preventing this is that the victims see the bullies as the „cool kids” (attractive, rich, strong) and want their approval. The victims see other victims as „losers” or „outsiders” and help victimise them, and the other victims respond in kind. The outsiders do not understand that what counts as „cool” is often a social norm. If the majority thinks behaviour, clothing or slang A cool, then A is cool, but if the majority agrees on B, then B is preferred. The outsiders face a coordination game: if they could agree on a new social norm, then their number being larger than the number of insiders would spread the new norm. The outsiders would become the „cool kids” themselves, and the previously cool insiders would become the excluded outsiders.

Finding new friends helps increase the number who spread one’s preferred norms, as well as insuring against future exclusion by any subset of one’s acquaintances.

If there are many people to choose from when forming new connections, then the links should be chosen strategically. People imitate their peers, so choosing those with good habits as one’s friends helps one acquire these habits oneself. Having friends who exercise, study and have a good work ethic increases one’s future fitness, education and professional success. Criminal, smoking, racist friends nudge one towards similar behaviours and values. Choosing friends is thus a game with one’s future self. The goal is to direct the future self to a path preferred by the current self. The future self in turn directs its future selves. It takes time and effort to replace one’s friends, so there is a switching cost in one’s social network choice. A bad decision in the past may have an impact for a long time.

It may be difficult to determine who is a good person and who is not. Forming a social connection and subtly testing a person may be the only way to find out their true face. For example, telling them a fake secret and asking them not to tell anyone, then observing whether the information leaks. One should watch how one’s friends behave towards others, not just oneself. There is a tradeoff between learning about more people and interacting with only good people. The more connections one forms, the greater the likelihood that some are with bad people, but the more one learns. This is strategic experimentation in a dynamic environment.

On backpackers and low-spending tourists

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Countries encourage tourism to make money. The same goes for local governments, tourism industry associations and tour firms. Some places provide options for low-spending tourists like backpackers, despite not making much money from them. These options may be cheap campsites, backpacker hostels, allowing hitchhiking and work-travel visas. At first sight, any positive revenue from poorer tourists would justify welcoming them. This simple revenue calculation, however, neglects the substitution effect and dynamic demand.

Substitution means that if cheaper travel options are available, then some tourists who would have spent more in the absence of these options now spend less. For example, a person who would stay in a hotel if there was no other accommodation, stays in a backpacker hostel instead. On the other hand, if all options are expensive, then the poorest tourists do not come at all. There is a tradeoff between the number of tourists and the average tourist’s spending. If introducing cheaper options leads to many tourists switching to these, but does not attract many additional low-spending people, then creating these cheaper options reduces total profit.

Dynamic demand means that a person who has toured a particular location once changes his or her likelihood of going there in the future. For example, having seen a tourist site, a person does not visit it again. Or someone going on vacation and liking the location starts going there year after year. If a region encourages young, low-income people to visit as backpackers, then it may increase or decrease future visits by these people when they are older and wealthier. In particular, if people do not tour the same location again (and spend more when older), then encouraging them to visit when young reduces the total profit from them over their lifetime.

The fact that some regions welcome backpackers has several possible explanations. There may not be much substitution, or a visit may increase future visits. The tourism industry may not have thought this through and may be reducing their own profit inadvertently. Or the government may have other objectives than taxes from the tourism industry. For example, allowing people from other countries to visit cheaply may make these people friendly to the host country, which may yield some nonmonetary benefit in international relations.

Raising grandchildren, not children

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Currently in all species I know of, each generation raises its children, who in turn raise their children, etc. This can be described as an overlapping generations model where each generation lives 2 periods, receives resources from the old of the previous generation in its youth and transfers resources to the young of the next generation when old. There is another equilibrium: each generation raises its grandchildren, has its children raised by its parents, and the children in turn raise their grandchildren. Instead of transferring resources to the next generation and receiving them from the previous, transfer resources two generations forward and receive them from two generations back. There are an infinite number of such equilibria: for each n, transfer resources n generations forward and receive them from n generations back. There are of course practical problems with large n, because the organisms do not live long enough to meet their level-n offspring.

There are complaints in developed countries that childbirth is postponed in life to acquire education and start a career. A possible solution is transitioning to an equilibrium of taking care of grandchildren, together with having children at a young age so that the grandparents are still alive to see the teenage years of their grandchildren. However, the equilibrium transition from taking care of children to taking care of grandchildren means that one generation must raise both children and grandchildren. The equilibrium transition in the other direction is easy – one generation does not raise its children or grandchildren, because its children are raised by its parents and its grandchildren by its children. Any other equilibrium is less stable than the raising-children one, because it is difficult to transition to it and easy to transition away.

The equilibrium stability comparision is similar to the social security equilibria in overlapping generations. In one equilibrium, everyone saves for their own retirement and consumes their savings when old. In another, every generation when young pays the social security costs of the previous generation who is old at the same time. The transition from the saving equilibrium to the equilibrium of paying the previous generation is easy, because one generation gets its savings and the contribution from the young, while the young do not save and receive the contribution of the next generation. The reverse transition is difficult, because one generation does not get a contribution from the young in its old age, but has to finance the retirement of the previous generation when young.

Smarter people have a comparative advantage in theory

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Theory research requires figuring out the result and how to prove it, and then writing these down. Empirical research requires the same, plus running the experiment or analyzing the data in order to prove the result. This requires relatively more time and less insight. If the production function of empirics requires in its input mix more time per unit of insight than the production function of theory, then smarter people have a comparative advantage in theory. They are endowed with more insight, but everyone has the same amount of time.
The amounts of theory and empirical research produced per unit of insight need not be related in any way for the above comparative advantage result.
Based on comparative advantage, I should switch to empirical research 🙂
Some empirical research methods are quite simple, but modern theory requires complicated math. Due to this, empirical research requires more time per unit of methods knowledge in its input mix. People with a stronger methodological background (better education) thus have a comparative advantage in theory. This suggests graduates of universities with more (advanced) coursework should be more likely to do theory.