Tag Archives: game theory

Avoiding an animal on the road

When a bike or car heads towards a squirrel, the squirrel first dodges to one side and then runs away in the other direction. Birds fly directly away from the oncoming vehicle, so stay in front of the vehicle for a few seconds. These behaviours are presumably evolutionary adaptations to avoid predators. For example, the squirrel’s dodge probably misleads a predator to alter course in the direction of the dodge. The larger predator then has more difficulty than a small agile squirrel in switching direction to the opposite side of the dodge.
In avoiding vehicles, these escape patterns are counterproductive. A predator tries to collide with the prey, but a vehicle tries to avoid collision. A squirrel’s dodge confuses the driver or cyclist, who then tries to pass the animal on the opposite side of the initial feint, which is exactly the direction the animal ends up running in. The best way to avoid collision may be to just keep going in a straight line and let the animal dodge out of the way. A constant direction and speed is easy to predict, which lets the animal avoid being in the same place at the same time as the vehicle. Keeping one’s course and speed also avoids accident-prone sharp turns and sudden stopping.
If a predator was smart and knew about the dodging behaviour, then it would go opposite the initial dodge. But then the squirrel would benefit from not switching direction. In response to the squirrel just running in one direction, the predator should run in the direction of the squirrel’s initial movement, etc. This game only has a mixed strategy equilibrium where the squirrel randomises its direction and whether it dodges or not, and the predator randomises its response to the squirrel’s initial movement direction. Dodging takes more energy than just running to one side, so the dodge must have a benefit that outweighs the energy cost, which means that the predator must be less successful when the squirrel dodges. Some factor must make it difficult for the predator to swerve opposite the squirrel’s initial direction. For example, if most prey keep running in one direction instead of feinting, then the predator may be on average more successful when following the initial movement of the prey. The cognitive cost of distinguishing squirrels from other prey must be too large to develop a different strategy for chasing squirrels.
The same game describes dribbling in soccer to avoid a defender. It would be interesting to look at data on what proportion of the time the attacker feints to one side and then moves to the other, as opposed to just trying to pass around the defender in the initial movement direction. It is more difficult for both players to switch than to keep moving in one direction, but presumably the player with the ball finds it relatively more complicated than the defender. In this case, to keep the other player indifferent, each player only has to switch direction less than half of the time, but the defender relatively less frequently. If the attacker feints and the defender does not switch direction, then the defender looks clumsy and the attacker a good dribbler. Reputation concerns of soccer players (who are after all entertainers) may make them switch direction more often than a pure winning motive would dictate.
Similarly, soccer players may use flashy moves like scissor kicks more often than is optimal for winning, because the flashiness makes the player popular with fans.

Neighbourhood coordinating to keep houses small and prices high

If apartment buildings are built in a neighbourhood of detached houses, then the house prices fall, especially next to the new apartment buildings. There is less privacy in the garden if many windows overlook it, and there is more congestion and crime if more people live nearby. The neighbourhood’s common interest may be to block the development of large buildings in it. However, an individual homeowner finds it profitable to sell to a property developer who will replace the detached house with a large apartment building, because the cost of reduced house prices is borne by the neighbours, not by the seller.
One way that neighbourhoods try to prevent this tragedy of the commons is to require all homeowners to join an association and agree to be bound by the rule that the association can prohibit new buildings or expansions. Such rule-based solutions are usually vulnerable to legal loopholes and changes in government policy that invalidate the restrictions. Game theory offers a solution without requiring any external enforcement: if one homeowner extends her house or replaces it with a bigger building, or sells to someone who will, then the neighbours respond by building apartment buildings around the property of the first breaker of the social norm of non-expansion. Then the view from the first expanded building is only the walls of the others, which makes the expansion unprofitable and deters enlargement in the first place.
The punishment for the first extension has to be certain enough to deter it. In particular, the homeowners next to the violator of the norm must be incentivised to build even at a loss. This incentive can be provided by requiring the neighbours of the homeowners next to the violator to punish those who do not punish the violator. This punishment can again be the development of large buildings next to their property. Those who refuse to punish the non-punishers can be punished the same way, etc, in concentric circles around the original violator.
The incentives provided by dynamic games such as this one may seem strange, but can be easily coordinated by a homeowners’ association without any legal power. The association simply publishes the rule that (a) enlargement of current buildings or the construction of new ones is forbidden and (b) if someone breaks the rule, then any new construction in a specified radius around the first rule-breaker is allowed. If one enlargement or new building is profitable, then typically a few extensions next to it are also profitable. The fewer neighbours of the first rule-breaker that build bigger houses as punishment, the more profitable an extension is for any neighbour. So some neighbours will punish the first violator. This will make the house prices of other neighbours fall, which reduces the cost to them of selling their houses to property developers for apartment building construction, i.e. reduces the cost of punishing the original rule-breaker.

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).

News are gradually biased by re-reporting

The (science) news cycle occurs when the original source is quoted by another news outlet, which is quoted by another outlet, etc, creating a “telephone game”, a.k.a. “Chinese whispers” familiar from kindergarten. Each re-reporting introduces noise to the previous report, so the end result may differ diametrically from the original story. This news cycle has been identified and mocked before, e.g. by PhD Comics.
The telephone game of news outlets has an additional aspect that I have not seen mentioned, namely that the re-reporting does not add random noise, but noise that biases the previous source deliberately. Each news outlet, blog or other re-poster has a slant and focusses on those aspects of the story that favour its existing viewpoint.
A single outlet usually does not change the story to the complete opposite of the original, because outright lying is easy to detect and would damage the outlet’s reputation. However, many outlets in a sequence can each bias the story a little, until the final report is the opposite of the original. Each outlet’s biasing decision is difficult to detect, because the small bias is hidden in the noise of rephrasing and selectively copying the previous outlet’s story. So each outlet can claim to report unbiased news, if readers do not question why the outlet used second-hand (really n-th hand) sources, not the original article (the first in the sequence). A single manipulator thus has an incentive to create many websites that report each other’s stories in a sequence.
The moral of this text is that to get accurate information, read the original source. Whenever you see an interesting news article, work backward along the sequence of reports to see whether the claims are the same as in the first report. The first report is not guaranteed to be true, but at least the biases and honest errors introduced later can be removed this way.

Signs with strong language are not enforced

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.

Scientific thinking coordination game

If most people in a society use the scientific method for decision-making, then telling stories will not persuade them – they will demand evidence. In that case, bullshit artists and storytellers will not have much influence. It is then profitable to learn to provide evidence, which is positively correlated with learning to understand and use evidence. If young people respond to incentives and want to become influential in society (get a high income and social status), then young people will learn and use the scientific method, which reinforces the demand for evidence and reduces the demand for narratives.
If most people are not scientifically minded, but believe stories, then it is profitable to learn to tell stories. The skilled storytellers will be able to manipulate people, thus will gain wealth and power. Young people who want to climb the social and income ladder will then gravitate towards narrative fields of study. They will not learn to understand and use evidence, which reinforces the low demand for evidence.
Both the scientific and the narrative society are self-reinforcing, thus there is a coordination game of people choosing to become evidence-users or storytellers. Note that using the scientific method does not mean being a scientist. Most researchers who I have met do not use science in their everyday decisions, but believe the stories they read in the media or hear from their friends. I have met Yale PhD-s in STEM fields who held beliefs that most people in the world would agree to be false.
One signal of not thinking scientifically is asking people what the weather is like in some place one has not visited (I don’t mean asking in order to make small talk, but asking to gain information). Weather statistics for most places in the world are available online and are much more accurate than acquaintances’ opinions of the weather. This is because weather statistics are based on a much longer time series and on physically measured temperature, rainfall, wind, etc, not on a person’s guess of these variables.

Salami tactics in everyday life

Salami tactics mean doing something others dislike little by little to keep them from obstructing or retaliating. Each small step is too small to be worth retaliation, but together the steps add up to an action that, if taken all at once, would definitely be worth stopping or retaliating for.
I have neighbours who put their unwanted things (broken bicycles, toys, furniture) in my parking space, using salami tactics. They don’t put the objects right in the middle of the space all at once, but initially put them mostly outside my parking space, with a small part of the object sticking into the space. If I don’t do anything, then the neighbours shift the objects so that a somewhat larger fraction of them is in my space, or add more objects that slightly stick into the space. If I push some of their rubbish out of my space, then other things appear, sticking into a different part of the space. They have plausible deniability in case I confront them – the object was only slightly in my space, so placing it there can be excused as an accident. This dance has gone on over a year, with them pushing their stuff into my space when I’m not there and me pushing it out when they are not there. Their encroachment attempts have become somewhat humorous, and I am observing them as a social science field study. The same encroachment happens in the common hallway, which fire regulations require to be clear at all times, but where the neighbours store their unwanted furniture. The furniture starts out near their door and gradually moves further and spreads out.
People in another house in this suburb have gradually squatted on a piece of the public park. They planted a hedge around that piece, which adjoins their dwelling. Now it is somewhat difficult to get into that part of the park (one has to squeeze through the hedge), so other people have stopped going there. It is effectively a private garden. The hedge did not appear overnight – the planting happened at a rate of about one bush per month, so it wasn’t too obvious to people who regularly pass through the park. The squatters planted the bushes in daylight, so deniability would have been a bit stretched if someone had confronted them. To some extent, planting one bush at a time in a public park can still be claimed an idle hobby, with no intent to encroach. However, the hedge that now clearly encloses a plot next to their dwelling does look suspicious.
A related tactic does not slice the salami slowly over time, but slices it many times at once to different people. At work, there are people who, upon receiving a task from the boss, ask one colleague at their level to help with one part of the task, another colleague to help with another part, etc, until they have delegated the whole task piece by piece. Each piece comes with an excuse why the delegator cannot do it. Then when the colleagues ask for help in return, the delegator is absent, unavailable due to family responsibilities or has some other excuse.

Signalling by encouraging good decisionmaking

Con artists pressure people into quick decisions. Marketing mentions that the offer is for a limited time only, so buy now, no time to read the small print. Date rapists try to get victims drunk or drugged. In all these cases, the goal is to prevent careful reasoning about what is happening and the decisions to be made. Also to prevent the victim from consulting others. Being pressured, confused or bullied while deciding is a danger sign, so one way for honest sellers to distinguish themselves is by encouraging good decisionmaking. Giving people time, referring them to neutral sources of info, asking them to think things over before deciding are all ways to make decisions more accurate.
More accurate decisions distinguish between good and bad deals better, which benefits honest sellers and harms con artists. This differential effect of information on good and bad types enables signalling by precision of information, where good types want to reveal as much as possible and bad types want to obfuscate. Information unravelling results – the best type has an incentive to reveal itself, then the second best type, then the third best etc. By not revealing, one is pooled with the average of the remaining types. In the end, the only type who does not strictly prefer to reveal itself is the worst type.

Raising grandchildren, not children

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.

Coordination game in choosing a university

The ranking of universities is very stable over time (http://m.chronicle.com/article/Rank-Delusions/189919) regardless of the difference in resources, scandals and other factors affecting popularity and quality. There are several positive feedback mechanisms keeping the rankings constant. These come from the multiple coordination games when choosing a university.
1) Smart and hardworking students want to be together with other smart and hard workers. If for some reason the best are in one location, then in the future all the best people have a motive to go to the same place. So the best arrive at that location and help attract other best people in the future. Similarly, party animals want to go to a university famous for its parties, and if many party animals come to a university, then it becomes famous for its parties.
Why would smart people want to be together with other intelligent folks? Just for interesting conversation, for useful contacts, collaboration. For these reasons, even the stupid may want to be together with the smart. Then an assortative matching results, as Gary Becker predicted for the marriage market (http://public.econ.duke.edu/~vjh3/e195S/readings/Becker_Assort_Mating.pdf).
2) Students want to go to a school with the best teaching staff, and the best professors want to teach the best students. I have yet to hear anyone wish for stupider students or teachers for themselves. Again the preference is the same among smarter and stupider students and professors, so assortative matching is a reasonable prediction.
3) The best professors want to be with other similar ones. Where there are such people, more will arrive.
4) Smarter graduates are likely to earn more and can donate more to the university. Then the university can hire better teaching staff, which in turn attracts better students, who donate more… The more talented also accumulate more power after graduating, in government institutions for example, which they can use (legally or not) to benefit their alma mater. Predicting this, again many people want to go there, and in the stiff competition the best get in.
5) If the employers believe that from some place, more intelligent people come than from elsewhere, then they are ready to make better offers to those coming from there. This makes the place attractive to all future employee candidates. Due to competition, the best get in, which justifies the belief of the employers.
6) Smarter people can be taught faster, at a pace that the stupider cannot keep. This mechanism gives everyone a motive to go to a school corresponding to their level.
7) Faster teaching means more knowledge during a standard length higher education, which the employers should value. The graduates of a school giving more knowledge are favoured, which makes the place attractive to everyone and leads to only the best getting in. The ability of the average student remains high, which enables faster teaching.