Tag Archives: game theory

Economic and political cycles interlinked

Suppose the government’s policy determines the state of the economy with a lag that equals one term of the government. Also assume that voters re-elect the incumbent in a good economy, but choose the challenger in a bad economy. This voting pattern is empirically realistic and may be caused by voters not understanding the lag between the policy and the economy. Suppose there are two political parties: the good and the bad. The policy the good party enacts when in power puts the economy in a good state during the next term of government. The bad party’s policy creates a recession in the next term.

If the economy starts out doing well and the good party is initially in power, then the good party remains in power forever, because during each of its terms in government, it makes the economy do well the next term, so voters re-elect it the next term.

If the economy starts out in a recession with the good party in power, then the second government is the bad party. The economy does well during the second government’s term due to the policy of the good party in the first term. Then voters re-elect the bad party, but the economy does badly in the third term due to the bad party’s previous policy. The fourth government is then again the good party, with the economy in a recession. This situation is the same as during the first government, so cycles occur. The length of a cycle is three terms. In the first term, the good party is in power, with the other two terms governed by the bad party. In the first and third term, the economy is in recession, but in the second term, booming.

If the initial government is the bad party, with the economy in recession, then the three-term cycle again occurs, starting from the third term described above. Specifically, voters choose the good party next, but the economy does badly again because of the bad party’s current policy. Then voters change back to the bad party, but the economy booms due to the policy the good party enacted when it was in power. Re-election of the bad is followed by a recession, which is the same state of affairs as initially.

If the government starts out bad and the economy does well, then again the three-term cycle repeats: the next government is bad, with the economy in recession. After that, the good party rules, but the economy still does badly. Then again the bad party comes to power and benefits from the economic growth caused by the good party’s previous policy.

Overall, the bad party is in power two-thirds of the time and the economy in recession also two-thirds of the time. Recessions overlap with the bad party in only one-third of government terms.

Of course, reality is more complicated than the simple model described above – there are random shocks to the economy, policy lags are not exactly equal to one term of the government, the length of time a party stays in power is random, one party’s policy may be better in one situation but worse in another.

Tradeoff between flashiness and competitive advantage in sports

Sports equipment is often brightly coloured, with eye-catching shape, such as for bicycle frames. Sometimes flashiness is beneficial, for example improving the visibility of a bike or a runner on the road, or a boat on the water. However, in sports where competitors act directly against each other (ballgames, racquet sports, fencing), eye-catching equipment makes it easier for opponents to track one’s movements, which is a disadvantage. For a similar reason, practical military equipment is camouflaged and dull-coloured, unlike dress uniforms.

Athletes would probably gain a small advantage by using either dull grey clothing, perhaps with camouflage spots, or equipment that matches the colour of the sports arena, e.g. green grass-patterned shoes and socks for a football field, blue or red for a tennis court. Eye-deceiving colouring would be especially useful in competitions based on rapid accurate movement and feints, such as fencing or badminton.

Another option for interfering with an opponent’s tracking of one’s movements is to use reflective clothing (mirror surfaces, safety orange or neon yellow) to blind the rival. This would work especially well for outdoor sports in the sunshine or in stadiums lit by floodlights.

One downside of dull clothing may be that it does not inspire fans or sponsors, so wearing it may reduce the athlete’s income from merchandise and advertising. A similar tradeoff occurs in real vs movie fighting. Blindingly bright equipment does not have this disadvantage.

Another downside of camouflage may occur if it replaces red clothing, which has been found to give football teams a small advantage. The reason is psychological: red makes the wearers more aggressive and the opponents less.

Golf as a cartel monitoring device for skilled services

Many explanations have been advanced for golf and similar costly, seemingly boring, low-effort group activities. One reason could be signalling one’s wealth and leisure by an expensive and time-consuming sport, another may be networking during a low-effort group activity that does not interfere with talking.

An additional explanation is monitoring others’ time use. A cartel agrees to restrict the quantity that its members provide, in order to raise price. In skilled services (doctors, lawyers, engineers, notaries, consultants) the quantity sold is work hours. Each member of a cartel has an incentive to secretly increase supply to obtain more profit. Monitoring is thus needed to sustain the cartel. One way to check that competitors are not selling more work hours is to observe their time use by being together. To reduce boredom, the time spent in mutual monitoring should be filled somehow, and the activity cannot be too strenuous, otherwise it could not be sustained for long enough to meaningfully decrease hours worked. Playing golf fulfills these requirements.

A prediction from this explanation for golf is that participation in time-consuming group activities would be greater in industries selling time-intensive products and services. By contrast, if supply is relatively insensitive to hours worked, for example in capital-intensive industries or standard software, then monitoring competitors’ time use is ineffective in restricting their output and sustaining a cartel. Other ways of checking quantity must then be found, such as price-matching guarantees, which incentivise customers to report a reduced price of a competitor.

Platform providers fake being popular

Crowdfunding platforms, stock exchanges and other providers of two-sided markets want to appear popular, because having more buyers attracts more sellers and vice versa. The platform’s revenue is usually proportional to the number of users, because it charges a commission fee on trades or advertisers pay it to show ads to users. The exchange’s marginal cost of a user is close to zero, giving it an incentive to fake a high volume of trades, a large limit order book and a small bid-ask spread.

The platform’s cost of posting a great volume of outstanding buy and sell orders at a small spread is that many investors try to trade at these favourable bid and ask prices. Either the market maker has to take the other side of these attempted transactions or is found fraudulent. Taking the other side results in a large loss if some investors are better informed than the exchange.

The platform could falsely display a large trading volume, but keep the order book honestly small by adding fake trades at prices between the bid and the ask only, so no investor’s real limit order is ignored. This seems difficult to detect, unless one side of the limit order book is empty (e.g. no buyers) and at least one at-market order on the other side (e.g. a sell) is outstanding. In this case, any trades occurring would have to satisfy the at-market order. However, the platform or real investors can then take the other side of the at-market order at a very favourable price to themselves, which discourages at-market orders. A large trading volume with a thin order book is still slightly suspicious, because it requires that crossing buy and sell orders between the bid and ask prices arrive almost simultaneously, in order to be matched without appearing on the order book for long, and without triggering the real limit orders. Displaying the fake buys and sells on the order book risks attracting actual matching trades, which the platform would have to honour (at a cost).

Without automated quote matching, there are no at-market orders, for example on the Funderbeam crowdfunding platform. Instead, everyone either posts a limit order or picks an order from the other side to trade with, e.g. a buyer chooses a sell. Investors can pick an order with a worse price (higher sell or lower buy) on the other side, which frequently occurs on Funderbeam. Choosing a worse price is irrational, unless the traders in question are colluding, so the asset is effectively not changing ownership. Reasons to carry out such seemingly irrational trades are to manipulate price and volume, e.g. price can be raised or reduced by targeted trades outside the bid-ask interval. Volume can only increase after added trades, rational or not, but such seemingly greater activity is exactly what benefits the stakeholders of the platform. The employees of the market maker have a natural motive to fake-trade between themselves to make their firm look good, even without any inappropriate pressure from their boss.

Another way to attract issuers and investors is to demonstrate successful initial public offerings, meaning that the funds are raised quickly (good for issuers) and the price of the newly listed stock (or other asset) goes up, which benefits investors. Adding fake capital-raisers is difficult, because potential investors will check the background of the supposed issuer. Inserting spoof investors into an actual funding campaign is costly, because real money would have to be invested. One way to manipulate popularity upward is to simultaneously add a fake issuer and fake investors who satisfy its funding need. The idea is to not leave time for real investors to participate in the campaign, by pretending that the capital-raiser achieved its target funding level before most investors could react. This is easier in markets with a small number of real investors and without an auto-invest feature. However, the real investors who were supposedly pre-empted may still research the supposedly very popular issuer.

A costless way to briefly boost the popularity of a real fundraising campaign is to add fake investors after the target funding is achieved, and forbid issuers from increasing the target or accepting funds from those who subscribed after the goal was reached. Any campaign meeting its target can then be made to look heavily oversubscribed. However, if the issuers are informed in advance of the restriction not to increase the target, then they may find an alternative unrestricted platform to raise funds. On the other hand, if the restriction is not mentioned beforehand, then it will likely anger the issuers who will then create negative publicity for the platform. Competition between exchanges thus curtails their manipulation incentives.

The platform can motivate real investors to raise their bids when the campaign reaches its target by rationing demand: bidders in an oversubscribed share issue get only a fraction of what they wanted to buy. Anticipating this, buyers will increase their requested quantities so that the fraction of their new bid equals their actual demand. This makes the campaign look oversubscribed and creates a feedback loop: if other investors increase their quantities, then rationing reduces the fraction of a given investor’s demand that will be satisfied, so this investor raises her or his requested amount, which in turn makes others increase theirs.

If investors know of the bid rationing in advance, then they may select a rival market provider without this restriction, but if rationing takes them by surprise, then they may leave and publicly criticise the platform. Capital-raisers compare exchanges, so if many market providers inflate demand and the issuers pay attention to the level of oversubscription (instead of the fraction of campaigns reaching the target, which is what should matter to the capital-raiser), then the biggest inflator wins. Of course, platforms may not want to reveal unsuccessful campaigns (e.g. Funderbeam does not), so public data on the fraction of issuers who achieved their funding goal is unlikely to exist.

Theoretically, the feedback from bid rationing to increased quantity demanded could lead to infinite amounts requested. A countervailing incentive is that with positive probability, other investors do not honour their commitment to buy, in which case a given investor may be required to buy the amount (s)he demanded, instead of the lower amount (s)he actually wanted. If there is no commitment to buy (for example, on Funderbeam the bids are only non-binding indications of interest), then the danger of overcommitting is absent, so the rational choice seems to be requesting an infinite amount. Investors do not indicate infinite interest, so either they are irrational or some other penalty exists for outbidding one’s capability to pay.

Star job candidates benefit from appearing to be worse

Employers have a cost of making a job offer: filling out forms, getting approval, not being able to make other offers simultaneously in case too many job candidates accept, etc. A company who believes that it is not the top choice of candidates would want to avoid making an offer to a star applicant (one who is likely to receive better alternative offers from top employers, thus turn down the lower-ranked company’s offer).

If the star job-seeker is uncertain about the offers she or he will get, or wants a bargaining chip to use with the most preferred company, then (s)he prefers to obtain the lower-ranked employer’s offer, even when planning to reject it. A way to entice the company into offering a job is to pretend to be more attainable (have a worse outside option) by faking lower talent and potential when interviewing with lower-ranked employers. For this pretence to be (partly) credible, it must have a cost for the job-seeker, otherwise all the best candidates would pretend to be worse and increase their chance of obtaining offers from their backup employers. Then the next-best candidates would have to fake being less good to receive jobs, etc. This race to the bottom would only end once all candidates look like the worst possible, which does not seem realistic.

One potential cost is that faking lower talent has a random outcome, which may be so bad that the employer does not want to offer a job at all. This would temper the incentive to appear worse. Another cost is information leakage – if bad performance at a less desirable interview becomes known to higher-ranked employers, then the candidate may forfeit her or his most preferred interviews and jobs. It could also be that the top job-seekers cannot hide their quality, for example because their genius shines out despite their best effort, or employers base offers solely on recommendation letters, which the candidate cannot see or affect around the time of applying.

Formal clothing is a bad equilibrium of a coordination game

What clothing happens to be considered formal is an equilibrium of a coordination game: if most others think that a given clothing item is formal, then a person who wants to be seen as formally dressed is better off choosing that garment. If enough people who aim to dress formally choose certain clothing items, then those garments will be interpreted as formal. Different cultures and eras have considered different clothes formal, e.g. tights for men were formal in Europe during Napoleonic times, but are not now.

Current formal clothing is a bad equilibrium because suits and shirts are difficult to clean, labour-intensive to iron or press, and restrict movement. A better equilibrium would be to interpret as formal some garments that are comfortable, environmentally friendly, easy to care for and cheap. It is unfortunately difficult to change equilibria in a society-wide coordination game, because a majority of people would have to change their beliefs in a short time.

The reason why suits are seen as formal is historical: these were fashionable at the height of the British Empire, which was the richest and the most powerful country in the 19th century, thus a trendsetter in the first era of globalisation. British fashion was copied in North America and Europe, spreading to the colonies from there. Labour-intensive clothes were a way for Victorian nobility to signal wealth, because only the rich could afford to hire enough servants to make and care for their clothes. In many cultures, wearing impractical clothes (toga, long dress restricting leg movemen) has been a way to signal that one does not have to work. Similar signals of leisure were pale skin (because most work was outdoors), soft clean hands (because most work was manual and dirty), straight posture (because work often involved stooping). More extreme signals of leisure were physical changes that made most jobs of that era and region difficult or impossible: women’s foot-binding in East Asia, mandarins’ long fingernails in China.

Contrary to pale skin demonstrating leisure in Victorian Britain, in modern developed countries, a suntan is a signal of wealth, because most work is indoors and most trips to tropical places or simply outdoors are costly and time-consuming vacations. A similar reversal of the meaning of a signal is that a fat belly showed wealth when food was scarce, but in modern developed countries with an obesity epidemic, developing an athletic physique takes time and effort, so being fat is statistical evidence of poverty.

Signals of wealth have always invited cheaper imitations. For example, solariums provide suntanning cheaper than travel to the tropics. Slimness can be faked with liposuction, a corset or less drastically with a tailored waist and vertical stripes that are closer together or narrower at the waist area. The appearance of broad shoulders is achievable by wearing a suit jacket with padded shoulders.

One reason for why a business suit looks the way it does is to make the man wearing it appear taller, slimmer in the waist, and broader-shouldered, thus more masculine and attractive. The V-shape formed by the lapels uses the well-known visual perception error that an object at the open end of a V looks larger than an identical object at the tip of the V. The front of a suit jacket thus creates the appearance of a slim-bellied, muscular man. If the wearer’s belly allows, then a suit jacket usually also has a tailored waist, which further visually narrows the middle of the body. The vertical lines created by the tie and the creases of the pants make the wearer look taller and slimmer, which is often accentuated by vertical stripes on the suit. It is very rare to see a suit with horizontal stripes.

The visual illusion of attractiveness that a suit creates provides a extra incentive to stay in the equilibrium in which suits are considered formal clothing. To ease the transition to a new equilibrium in which the clothes perceived as formal are more practical, the new formal clothes should improve the wearer’s looks even more than a suit. This is not difficult, because many garments may have V-shaped patterns printed on the upper body, vertical stripes on the lower, have a tailored waist and shoulder pads. The patterns and cut may be designed based on psychology research to maximise the athletic appearance of the wearer. Anything achieved with a suit may be replicated and further optical enhancements added, for example printed outlines of muscles and puffed upper sleeves.

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.