## Signaling – Show that you can, show that you mean it

My previous post was about complete and incomplete information and about revealing your advantages to your opponents to gain an even bigger advantage. I finished with a short discussion on signaling: How to credibly differentiate yourself from others to gain a higher payoff?

In his course on game theory, Ben Polak represents a good example on signaling by using a simplified model of the job markets. Here I represent it, with possibly different figures, but the idea holds:

• There are two types of workers only: good and bad
• 10% of all workers are good, 90% are bad
• a good worker produces 50 dollars worth of goods per day a bad worker produces only 20 dollars worth of goods
• employers cannot tell the difference between a good and a bad worker before hiring them
• the two types of workers are otherwise identical, just their output is different
• this game lasts only one day, to keep the calculations simple

On average, an employee produces 23 dollars worth of goods, so the average salary level is also 23 dollars. Therefore, the bad workers earn slightly more than they produce, and the good workers a lot less than they produce: a good employee would earn 50 dollars if he could signal credibly to the employer that he is a good worker. Of course, a bad worker would also want to earn 50 dollars instead of 20 or 23. Thus we need something to differentiate between the two, we need a signal.

A signal that differentiates the good workers from bad workers, or any types from one another in general, has to be such that good workers will always give the signal and bad workers will never give the signal. For a signal to be credible, it’s costs obviously have to be such, that they reduce enough the net salary of a bad worker, but do not reduce too much the net salary of a good worker: this way the bad workers will not be willing to give the signal while the good workers will always give the signal.

As an example of a signal, Mr. Polak mentions the possibility of dancing on the table in a job interview and singing a song about how good an employee you would be. Such a signal is obviously costly, being humiliating at the very least, but it does not help differentiate the two types of workers. After all, it is equally humiliating for both types, so even if a good worker would have the incentive to give the signal, the bad worker would have the same incentive, in order to be identified as a good worker and thus receiving the salary of 50 dollars. Clearly not all costly signals can separate the worker types from one another.

Education as a signal

It turns out that education is a form of signaling and conversely, among other things education has a role as a signal giver at the job market. Let’s introduce a two-year MBA that either type of worker can take. The costs of tuition are the same for both and so are those for housing, transport and food. We might argue that the two types have different opportunity costs in taking an MBA instead of working, but both types would earn 23 dollars since we do not yet have a signal to separate them at the job market. So why does the good worker do the MBA and the bad worker doesn’t, as I am proposing? The difference in the costs is the effort, the mental work, hours of sitting in lectures doing homework and assignments. For the bad worker the required effort to finish the MBA degree is much higher than for the good worker. So much, that receiving an MBA would reduce his net salary below current levels, even below 20 dollars.

Of course, in this example the figures can be forced to be in such a relation to one other that the signaling works. E.g. if we make the total costs of an MBA, including the effort, to be 10 dollars per year for the good worker and 20 dollars per year for the bad worker, it is obvious that the good worker will do the MBA and receive a net salary of 30 dollars after being identified as a good worker and hired by an employer. Conversely, the bad worker will not take the MBA, since his net salary for doing an MBA and being identified as a good worker is 10 dollars, which is below the 20 dollars he would receive otherwise.  In addition, the employers have to believe that good workers, and good workers only, take an MBA. Otherwise the good workers might, regardless of their MBA, be identified as bad workers reducing their incentive to take an MBA.

Even if the figures in the above example are arbitrary, the main point is that the signaling mechanism has to be such that it will provide reliable signals and no type has the incentive to deviate. Thus, when creating the mechanism, the related figures actually have to be chosen in such a way that the signaling is reliable and adjusts the payoffs properly. In our MBA example a one-year MBA would not suffice, since a bad worker would do the MBA and receive a net salary of 30 dollars, instead of the 20 dollars he would receive otherwise. On the other hand, a one-year MBA could be made a lot harder and work-intensive, so that the per-year costs are increased and, again, only the good workers go for the education.

Signaling in other areas of life and work

Signaling is not only useful and used in employee-employer relationships. For example, buyer-seller interactions might also require, or at least benefit from, signaling.

For example in the case of used cars information imbalance between the buyer and the seller can lead to all goods in the market being of poor quality. In such a case, the potential sellers of higher quality products would have to be able to reliably signal this quality to the potential buyers. The buyers do not have to signal their preferences, since a buyer looking for higher quality products will buy one, if he gets more value from it, and nobody will pay for a good more than the value received from buying and possessing the good. Thus, we do not have the potential problem of customers looking for low quality products suddenly hoarding all the high quality products.

Another interesting realm where signaling can be applied is the one of procurement. At least larger companies often have a centralized procurement function that is responsible for managing the main suppliers, conducting supplier selection and awarding contracts. When looking for a supplier, the procurement function has to create competition between the candidates to find out the best one for the given quality and specifications. However, a potential supplier must invest resources in the bidding process without any certain revenue or supply contract. If the potential supplier thinks that the expected payoff from the contract is low, he will not put too much effort in to the bidding. This might lead to the customer company receiving only a few offers or the offers being of poor quality and difficult to compare against one another. To increase the number and quality of the offers, the customer company would have to signal, in a reliable way, that the potential contract has a guaranteed, maybe even high value. The way to do this is to commit, before the bidding starts, to awarding the contract to one bidder and to one bidder only, and beforehand abstaining from any cherry picking between offers. This of course requires that a large enough pool of bidders is invited and that the background research on them has been done, since procurement will have to commit to one of the invited bidders. Therefore, their capabilities have to match the requirements well enough, so that in principle any solution could be accepted.

As we see, tying your hands or incurring costs to show your commitment and capability are some ways to reliably signal who you are. Consequently signaling can help you leverage those advantages that might otherwise go unnoticed. Information is power, and shared information can be overpower.

## Incomplete and complete information – Strengthen your advantage by revealing it

I have nearly finished the Open Yale course on game theory. Just the final exam is still to be done. Although my exam won’t be graded, I’ll use the opportunity to tackle those problems with the new tools and mind-set and see, what I have learned and understood.

The last topics in the course were about incomplete information and signaling. In game theory incomplete information refers to games, where at least one player is uncertain of the other players’ so called types. A type describes a player’s preferences, available strategies and payoffs. For example, in a real life negotiation we often have incomplete information, being uncertain how tough the opponent is and how he values the potential outcomes. A related concept, imperfect information, we have already encountered when a player does not know, which strategy his opponent has played, although he knows all the potential ways the game could be played and the related preferences and payoffs.

Incomplete information is a realistic condition and thus often encountered when modeling real world phenomena. Often incomplete information is also seen as an asset from the informed party’s point of view: for example, a company knowing both its own and its competitor’s cost structure is intuitively thought to have an advantage, since it knows more, and information is power, as the cliché goes. But what exactly is the benefit of knowing your competitors’ costs and how valuable is it? A further question, with an even less intuitive answer, is, whether such a better-informed company would actually profit from making its own cost structure public. In the following, I will answer these questions from the perspective of the Cournot duopoly model, but taking it a bit further from the standard treatment.

The following is based on the Open Yale course Econ 159a Game Theory and on Strategies and Games: Theory and Practice, 1999 by Prajit K. Dutta.

Incomplete information in a Cournot duopoly

In the standard Cournot duopoly two profit-maximizing companies manufacture substitute products with identical constant marginal cost and serve the same market. The outcome of the model is that in equilibrium both companies produce the same amount of goods, in total more than the monopoly quantity but less than the quantity in free-market competition. Consequently, the companies also get higher than free-market prices and profits, but not the monopoly prices or profits due to the competition between the two rivals.

In an incomplete information Cournot duopoly at least one company (I will only consider this case in the following) has its marginal cost different from those of its competitor’s and this exact cost is unknown to the competitor, while the competitors marginal cost is known by both parties. On average, the company with non-public marginal cost has the same marginal cost as its competitor and the competitor knows this. In equilibrium, the company with the unpublicized marginal cost produces more, reducing the market price, and gets higher profits when its marginal cost is lower than the average. If its marginal cost is above the average, its produced quantity, the price and its profit move to the opposite directions. Somewhat surprisingly, if the company can without costs and credibly reveal its lower marginal cost to the competitor, it will benefit even more, while a company with above average marginal cost would suffer even more.

In table 1 I have summarized the produced quantities, prices and profits to show that revealing its lower than average cost structure in a Cournot duopoly is indeed beneficial for a company. The intuition is the following. When the low-cost producer (company 2) does not reveal its marginal costs, the competitor (company 1) reacts based on the average marginal cost, producing the standard Cournot-quantity. This is the logical reaction, since on average company 2 has the same marginal cost as company 1. However, company knows its own cost structure and produces more than the standard Cournot-quantity, since this is profitable due to the lower than average marginal cost. Likewise, a high-cost company 2 would produce less than the standard Cournot-quantity, but would not suffer from its competitor’s producing more than its standard Cournot-quantity, since again company 1 is reacting as if company 2 had the average marginal cost.

If company 2 could credibly make its lower than average marginal cost public, company 1 would know that company 2 can and will produce more due to its lower marginal cost, driving the price down. In this case company 1 would react to the actual lower than average marginal cost of company 2, not on company 2’s expected average marginal cost. Consequently, company 1 will produce less to counter the price erosion and maximize its margins in this situation. Also, knowing the reaction of company 1, company will produce more, making also higher profits than in the case of incomplete information. Correspondingly, a high-cost producer will also suffer more if its cost structure becomes public, so it will try to keep this information secret.

Table 1 summarizes the Cournot-quantities, prices and profits in different cases of a Cournot duopoly, with companies 1 and 2, company 2 being the low- / high-cost producer who always knows company 1’s constant marginal cost. In the table I have used the following notation:

• P = a – bQ > 0, where P is the unit price a and b are non-negative constants
• Q = Q1 + Q2, where Q1 and Q2 are the quantities produced
• c is the average marginal cost
• ε is the difference of the low-/high-cost company’s from the average marginal cost
• c + ε > 0
• a low-cost company 2 has ε < 0, a high-cost company 2 has ε > 0

I have also used P’, P’’ and similar expressions for the quantities to separate the cases of standard Cournot duopoly from those of incomplete and complete information with company 2 having lower or higher than average marginal cost.

From table 1 it becomes clear that profits for company 2 increase (decrease) for negative (positive) values of ε, when we move from the standard Cournot duopoly to a duopoly with different marginal costs between companies with incomplete and finally complete information. Thus, a cost advantage is strictly profitable and making it public increases the profit. The profits of company 1 decrease (increase) for negative (positive) values of ε,  when moving from the standard Cournot duopoly to a duopoly with different marginal costs between companies with incomplete information. Thus, a cost disadvantage of one company is strictly profitable for the other companies and their profits increase with this cost disadvantage. With some algebra, it can be shown that company 1’s profits in the case of complete information are lower than in the case of incomplete information and that the difference is (ε/6)*(a + c + 2ε), which is negative (positive) for negative (positive) values of ε.

As argued previously, a low-cost producer in a Cournot duopoly has the incentive to make its cost structure public to maximize its benefits, i.e. profits. More precisely, the producer with the lowest marginal cost has this incentive, since non-disclosure would lead the competition treating the company as an average-cost producer. Therefore, the producer with the lowest marginal cost will reveal its costs. Now, if there are more competitors in the market, the producer with the second lowest marginal cost also has the incentive to reveal its costs, although they are higher than those of the cost leader. If the producer with the second lowest marginal cost did not reveal its costs, it would now be treated as an average producer in the remaining group of companies: the lowest cost producer has now been excluded from the average, since its cost structure is known. But being treated as an average-cost producer is clearly sub-optimal, if a company’s marginal cost is below the average. Thus, the producer with the second lowest marginal cost will also reveal its costs. This logic can be followed right to the last company on the market, to the one with the highest marginal cost.

When one company, the one with the lowest marginal cost, reveals its costs, this leads to information cascading, since the companies with the next lowest costs now want to differentiate from competitors with higher marginal cost, even if they have costs above the average over all companies at the market. This makes the marginal costs of all companies public, or at least their relation to one another. The last company is evidently going to be the one with the highest costs, since it wishes to stay hidden among the masses and has thus not yet revealed its costs. It follows that the last company does not have to reveal its costs; the competition will be able to infer, that the last company has the highest marginal cost and will react accordingly, even if not knowing the exact costs.

The dog didn’t bark – the value of undisclosed information

The previous exercise shows an important, broader real-world application of revealing information. The absence of evidence or the absence of information can be a substantial piece of information. If a company does not want to reveal its cost structure, it is likely due to its high (marginal) costs, at least in the context of the Cournot duopoly model. But not all markets are like the Cournot model, so the implications are not completely generalizable. But still, even in a free market where all companies are price takers, revealing your costs might help you; not in gaining market share, since your produced quantities do not affect the prices, but in keeping competitors from entering price wars. By revealing your costs, you can potentially indicate that you have the largest margin and can thus come out on top, should a competitor start a price war. But by revealing your costs, you may be able to keep your opponents at bay, since they know in advance that their chances of winning a price war are slim.

The difficulty in revealing the costs and gaining the associated advantage is that it is not always evident, which company has the lowest costs. Therefore, companies may restrain from revealing their costs, even if they would benefit from their low costs more when if became public. But without knowing that it is a low-cost producer a company risks becoming disadvantaged, should it in fact be a high-cost producer.

In the case of very similar consumables and bulk goods (e.g. oil, agriculture products) good estimates on the relative costs among competitors may be made and thus own cost advantages can be made public to keep the competition from starting a price war. For highly specialized and small-series products with small markets, revealing a cost advantage would give the power to affect the demand, prices and quantities produced, but finding out who is the low-cost producer might be more difficult. Specialty products often enjoy higher margins, so that product prices are poor indicators of true costs.

In conclusion, revealing information to your rivals may give you an advantage, and not revealing information already conveys information about your situation. Furthermore, even if you are not in the best position in a group of competitors, being able to separate yourself from the even weaker ones may give you an advantage, and to do this you must credibly signal that you have an advantage over some of the competitors. This will then lead to all with a relative advantage to revealing this information.

Signaling is yet another topic in game theory and discusses how different types of players, e.g. good and bad workers, can credibly be identified: an employer has an incentive to get the good and, presumably, more productive good workers, and the good workers have the incentive to reveal themselves in hopes of a higher salary. But the bad workers also have an incentive to be taken for good workers, due to the potential higher salary. Therefore, if the higher workers are to earn more and employers are to pay “correct” wages to the two types of workers, we need a credible signal that the good worker can and will give, but the bad worker cannot or does not want to give. I will return to this topic in my next post.

## Food and agriculture – feeding the globe

In the beginning of June The Economist published an interesting article on the future of agriculture and how new technologies can help improve yields and reduce the required resources for food production. The growing world population requires more food and climate change may take its toll on agriculture. Among the examples for getting better harvests and increasing efficiency in food production were the use of GPS for more directed fertilizing, gene technology as a means to improve yields and make crops resistant to disease and big data analytics to analyze the effects of selected technologies on food production.

The article discussed how food production can be made more effective and efficient, but it also provoked thoughts in to the direction of equality and food consumption.

In the article was the below graphic from the Food and Agriculture Organization (FAO) showing the estimated global consumption of calories per capita and food source by 2050.

What struck my eye was the estimate on food intake of about 3´000 kilocalories per person per day in 2050. Based on the same graphic, that is an increase of about 13% from the 2010 level of roughly 2’650 kilocalories and an increase of 25% from the level in 1970. Yet, we certainly are not more active on average, and a large portion of the population is doing office work, a trend unlikely to see an end any time soon as robots take over the more physical tasks.

The Economist cites a FAO report from 2009 that estimated the required increase in agricultural production to be 70% in order to meet the forecast demand induced by increases in global population and food intake per capita. The Western World is already battling with obesity and the developing economies are, unfortunately, catching up, so the required increases on food production could be more moderate, if we put more effort into keeping ourselves at a healthy weight and eating what we need instead of what we want. As the FAO estimates the world population to be 9.7 billion by 2050, just keeping the average caloric consumption at current levels would require an increase of 30-40% in the global food production based on the population growth of 2.4 billion from today’s 7.3 billion. This would require only half of the growth required to meet also the increases in expected average food consumption per capita.

Wasting food, saving time

The technological advances in farming technology, gene technologies, aquaculture and other related fields might be enough to increase food production as required by the increasing population and the growing average food consumption. But I think it would be irresponsible to use all that technological capacity regardless of whether we actually need it or not to feed the whole world adequately. If we make more and more food available, even with the same resources, we either end up eating more with stable or even reduced activity levels, inducing obesity, or we end up wasting more of the food if it won’t be eaten. The first option would be undesirable since all we end up with is more obese people who have to be treated. This would lead to increased costs in health care, and these costs are avoidable just by avoiding eating all that much.

The second option, more food being available and more going to waste is not necessarily a bad option. For example, if the availability of food reduces people’s time spent on doing grocery shopping and the time required “for finding food”, the benefits may overweigh the costs of the wasted food. If a high-skilled person can use this extra time to do productive work and the value of his output is higher than the value of the wasted food that is allocated to him, it is clearly beneficial to have an abundance of food and throw part of it away. The problem here is that such an analysis, especially on a global level is not trivial: How much time each person can spare? How will the person use this time? What is the value of the activities and their outputs that came out of this extra time? How can we even measure the value of these outputs coherently? Is it morally acceptable to use food for time optimization in some countries when others have their people starving?

The above questions are just some that we would have to answer, but I think that any economist worth his bread could give at least an indication how to approach the problem. Gaining global commitment and coordination for such endeavors is yet a further complication.

Food for the hungry, food for thought

Whether or not we will use new technology to improve our global productivity by making food more readily available to all, I think it is clear that famine, malnutrition and obesity are problems that have to be solved in any case.

Since we already have, on average, enough nutrition to feed the whole world, maybe we should use the technological advancements selectively to distribute the available food and nutrition more equally and efficiently. This can take place either locally by use of better farming methods or via centralized farming and global logistics, depending on which alternative if more effective and efficient.

In 2013 FAO estimated in its report on food and agriculture (see page 5 of the report) the global costs of undernutrition and micro-nutrient deficencies to be 2–3% of the global GDP of some USD 70–80 trillion, and the costs of non-communicable diseases, for which overweight and obesity are key risk factors, to be in aggregate about 2% of the global GDP in 2010 during the following two decades. Clearly, undernutrition is still the larger problem, by a factor of 20, yet the increasing obesity problem all over the world should be tackled now, before it becomes, well, bigger.

As I see it, undernutrition and obesity can be partially targeted with complementary methods. Undernutrition is caused by too little high quality food, while obesity is caused by too much food in relation to activity levels, and the food eaten might also be of inferior quality, lacking in nutrients. Therefore, the key would be to improve the general nutritional quality of consumed food all over the world. I am not going to start a lecture on sugary drinks and high-fructose corn-syrup, but they are admittedly in the center of the discussion, when it comes to low-quality food. The total cost aspect of nutritious food and increased activity levels leading to reduced health care costs is also an important point in this discussion.

As other areas of life, we might and should think food and physical activity as daily choices. Life goes on every moment and waiting for the right time to do things or start something is useless; it’s never the right time, so we should start now. Likewise, our daily food choices and activity are what keeps us healthy, not some miracle diets and fitness programs that are waiting to be started in the future.

What am I doing to help? Currently, just minding my daily choices. As Gandhi said, “Be the change that you wish to see in the world.” If you wish for more active people, be more active. If you wish people ate healthier, eat healthier.

## Sequential games and backward induction

My studies on the Yale web course on game theory have progressed again. The latest topics were sequential games and, as Mr. Polak put it, one of the most important concepts one might learn at Yale, backward induction.

Sequential games are games, where one player takes action first and the second one acts afterwards, knowing what the first player did. Both players also know, that the game is sequential and that the first player’s action and its results will be known to the second player before he takes action.

The key to solving sequential games is backward induction, a concept that is quite simple and very powerful. The idea of backward induction is to picture the end of the game, the last move. Whoever makes the last move, will want to maximize their payoff, as usual. When the last move is found out this way (there are potentially many options), the move before that can be solved, when considering the payoffs of the player making the second to last move: when this player knows that the player going last will maximize his payoff, he is under a constraint when maximizing his own payoff. Similarly we can work our way backwards to the beginning of the game and anticipate the first move, too. Sequential games are often modeled as decision trees.

Although backward induction is in principle easy to use. building a decision tree may be impossible due to the infinite number of possible strategies players might play. However, in such cases it may be possible to use other tools, such as calculus in optimization problems, to find out the best responses using backward induction.

In addition to backward induction, Mr. Polak also discusses moral hazard, incentives, commitment and first-mover advantage in his lectures 13 and 14. In summary the most important lessons, apart from backward induction, are:

1. Moral hazard can prevent players from reaching the best possible outcome, since their incentives are not aligned, e.g. a creditor and a debtor.
2. Tweaking the game and the incentives, e.g. by reducing the payoffs of some strategies, mutually better outcomes can be achieved, as incentives become aligned, e.g. a collateral for debt reduces the risk of default.
3. If in a sequential game you make a public, irreversible commitment to play a certain strategy, you may force your opponent to play a certain strategy, thus securing your own payoff, e.g. a company announcing to build a new plant before their competitor and consequently increasing the market capacity to 100%, and also winning market share.
4. First-mover advantage is not always prevalent, and sometimes there is a second.mover advantage, e.g. in a sequential version of rock-paper-scissors. Sometimes one might also inadvertently make oneself into the second-mover and lose the sought first-mover advantage.

For you to remember the most important of the concepts just presented, I will repeat it one more time, backward induction. Its the answer to all questions, as Mr. Polak mentions during his lecture 13.

## Game theory – Mixed strategy equilibria

On the Yale web course on game theory by Ben Polak I have learned about Nash equilibria (NE) and also mixed-strategy NE. In lecture 10 Mr. Polak explains very well three different interpretations for a mixed-strategy equilibria by an example of paying taxes versus avoiding them. A mixed-strategy NE either:

1. is a combination of randomized pure strategies played by an individual,
2. reflects our expectations on how our opponent is going to randomize and deploy his pure strategies or
3. is the proportion of people in a group each playing a single pure strategy.

My payoffs define your strategy mix

I have had to spent quite some time to really understand the concept of mixed-strategy NE, namely that my strategy mix is dependent on the payoffs of the other player and vice versa. Furthermore, changing my payoffs does not change my strategy mix but that of the other player, a concept that also seems at first somewhat counter-intuitive. The subtle point here is that neither I or my opponent is trying in any way to force the other player into the mixed-strategy NE, rather if we are to be in a mixed-strategy NE, then one player’s strategy mix is based on the payoffs of the other player, and neither player can do strictly better by deviating from his chosen strategy mix.

In the example of tax paying and tax audits (as described by Mr. Polak in the video), a mixed-strategy NE reflects the interpretation 3, different groups of people each playing a pure strategy. In case of taxes, the people playing the pure “tax evasion” strategy can be expected to be people benefitting the most from evading taxes, while those playing the pure “pay taxes in full” strategy can be expected to be those who have little to gain from tax evasion. Based on this idea Mr. Polak presents an argument of why increased penalties for tax evasion do not increase compliance on paying taxes.

Auditors’ payoffs effect tax compliance, penalties do not

If legislature is amended to increase the penalty for the evasion of income taxes, it does not increase the compliance for paying taxes, rather it decreases the number of audits. When a tax payer’s expected benefit from tax evasion is reduced (by increasing the penalty for tax evasion), less audits are required to reach an equilibrium state where an individual is indifferent between paying his taxes and evading taxes, when he might or might not be audited. Conversely, if the benefit from tax evasion increases, tax compliance, according to the model, does not deteriorate, rather more audits are conducted (on rich people) to keep the game in an equilibrium.

To increase compliance, the auditor’s payoffs would have to be increased. When increasing the penalties for non-compliance, the auditor’s payoff does not change Therefore the auditor has no added incentive to try to catch the people evading taxes. The auditor also has no incentive to realign his resources accordingly to increase the probability of finding tax evaders with the audits he is conducting. However, if an auditor’s payoffs for finding tax evaders are increased, he has the incentive to find them and will also re-align his resources accordingly. This will increase the probability of tax evaders being caught and thus increases compliance among those who have the higher incentives to avoid paying their taxes.

If the above seems unclear to you, I must admit that I am still myself struggling with these concepts. By writing them out I am trying to clarify my own thinking and hopefully give you some insights, too. One big lesson for me has been, that by applying game theory to common scenarios and everyday questions, we may get new insights and understand, why some actions and policies do not have the effect we might initially expect them to have.

## Nationalities and athletic performance for sale

Reading the newspapers this weekend, I spotted an article on a topic that has gone under my radar: buying athletes to gain success in international sports competitions. With buying of athletes I am not referring to illegal bribery, but to the practice of sponsoring a foreign athlete and having him consequently change his official nationality to that of the sponsoring country. This practice is nothing new, but has become more prevalent in recent years, as nations want more fame and fortunes. It is not just countries looking for the best talents but also athletes trying to find the best opportunitiesSome voices say that these practices of nationality and athlete shopping are worrying, if not outright morally wrong.

A knee-jerk response to the question on the fairness of these practices might be to condemn them as immoral since sports is about fair competition between nations and should be not driven by motives other than the joy of sport and competition.

When looking at such a counter-argument, as I present above, for trading athletic skills for money, it seems to be on shaky grounds. What is fair competition? Why should sports be done only for the joy of sport and competition? Yet another question is, if it is even relevant or desirable for nations or countries to compete against each other in sports. I will briefly discuss each of these questions and after that, I will draw the argument together with some analogies to the business world.

Sports and fair competition

If we say that sports, and especially sport competitions between nations, should be fair, I suppose we are requiring equal chances to win, equal chances to exploit potential or something similar. Without going too deep into a philosophical discussion on fairness, I just want to point out that even the concept of fairness is vague and not unlikely to vary between individuals. It is obvious that everyone prefers a “good” or “successful” life to a “bad” or “unsuccessful” one. Yet, we are not equally successful. But whether the observed inequalities are fair or unfair, is not always to decide. For those interested, I recommend reading John Rawls who has intensively studied fairness. In reading Rawls, it becomes clear that even equal chances to use our natural talents may not be fair. Thus, the requirement of fairness in sports would need a more rigorous definition to provide a good argument. In any case, I would claim that it is acceptable to pursue activities which you like, are good at and for which people are ready to pay.

Sports for the sake of sportsmanship

One argument against countries’ buying athletes into their national teams and athletes shopping for better prospects might be the concept of sportsmanship, the idea that sports is something pure and pursued just for its own sake. My immediate counter question is, why it should be so.

Many of us do sports, gymnastics, weightlifting, horseback riding, running, skiing and so on. Some of us train for health and fitness or to challenge our own limits. Some train for competitions where they can measure their skills against those of others. I’m inclined to think that many of these reasons belong or at least relate to the concept of sportsmanship, but they might just as well be goals on their own merit. We may play football on a Sunday afternoon with our friends just for fun, to spend time and rejuvenate from the hard workweek. But even then, I would argue, the purpose of the football game is to mingle with friends, recuperate and regain strength. These are stronger motives than just playing football for footballs sake.

The aspects of respect, ethics and fairness related to sportsmanship play a role in how we treat others during sports, but shouldn’t we always treat others with respect and according to high ethical standards? If we are to use these ideals to limit the number of ways how sports is to be pursued, why shouldn’t we also apply them in other areas of life? Why would it be any more acceptable for an office worker to move abroad after a better job and eventually change his nationality than for an athlete? I would argue that it is in both cases acceptable to maximize the benefits you can gain from using your skills, assuming that you are doing within the limits of the law.

Finally, the concept of fairness is still somewhat vague, so the concept of sportsmanship leaves us without a solid argument against our question on nationality shopping.

Utility and the competition of nations

The Olympic games are maybe the best example of a sports event where nations stand to find out who runs faster, jumps higher and is the stronger one. Winning sports competitions gives good publicity for countries, abroad and domestically. The politicians of a country with troubles in its internal affairs may receive a welcomed boost for their image, if their home country is successful in the Olympic games or other high profile sports events. Likewise, the individuals winning the respective competitions gain publicity, receive fame and fortune and can hope for even better opportunities in the future, as advertisers want to use them to increase sales, or the athletes can use the publicity to become known professionals in other areas of life.

Winning sports events can be seen as a consumable good like anything else, and people (and nations) have different preferences for goods. For example, ice hockey is quite liked in the USA and Canada so those countries have a high interest in getting the best players into their national teams, although their domestic supplies are already ample enough. Analogously, in Germany football enjoys high popularity so Germany could be argued to have a high interest in getting good football players into its national team, although here again the domestic supply is high enough. The main point is that if a nation receives benefit from trading something else for better performance in a sports activity, within legal boundaries, it should not trouble other countries. If some countries are willing to make that trade, two countries benefit. There might arise externalities that reduce the utility of other countries, but that can take place whenever people change their home country. Therefore, athletes changing country or nationality should not be seen as a special problem when compared to people in other professions.

As the people in today’s world are connected with each other, and people from different countries work together, the old meaning and purpose of nationality seems less important. Does it then matter, if an athlete has little or no connections to the country he is representing? Companies hire consultants to work for them, mainly to benefit from the consultant’s expertise. Companies also cooperate with celebrities for marketing purposes, paying for the use of a celebrity’s fame in hopes for increased sales. But these consultants or celebrities do not necessarily have any deeper connection to the company that is just one client among others. Likewise, an athlete could treat a country as a client, who buys his services in hopes of increased fame, visibility and financial benefits.

Pursuing talent in sports and business

We often hear about successful companies and their managers, but the home countries of these companies are less often at the center of the view. Countries may of course provide good policies, legislation and infrastructure for companies to flourish, but it is in the end the company that gets the most credit for its own success. Why shouldn’t this be the case with athletes? Furthermore, why shouldn’t countries try to get the best athletes into their teams and athletes go and grasp the best possibilities they are offered?

Countries try to get companies to invest in them, and individuals take jobs in those companies and countries that give them the best prospects. Since an athlete’s job is to compete in sports and, at least to some degree, entertain the audience, why shouldn’t he look for the best possible employer and the best possible country for pursuing his profession? On the other hand, why shouldn’t a country try to improve its success in the field of sports by offering good working conditions for athletes and recruiting talents from abroad? If we still accept that everyone wants a good life and that it is acceptable to maximize the benefits from your profession and if we also add the premise that a good life entails some degree of material well being, the conclusion is that athletes should be allowed to change their nationalities if they are so better off. Likewise, countries should be allowed to offer athletes citizenships. This all of course assumes that the actions take place within the boundaries of the law.

Who gets the spoils?

One piece of criticism against athletes changing their citizenship is the fact that their parents may not be following them, but stay at their, possibly poorer, home country.

But don’t all parties benefit, if a young talented athlete represents a foreign country, is paid well and can use his money to help his parents in his poor home country? This same practice takes place among people who are doing other jobs, coming from poorer to richer countries and sending money back home to help their families.

Arguably the initial media publicity from winning a sports event and the ensuing benefits in reputation and the monetary goods go mainly to the country an athlete is representing, but depending on his contract the athlete may be able to represent his home country later on. And when asked about his background, the athlete is able to promote his original home country, so it is not obvious that the arrangement would not be beneficial to all.

Even if money is not the main question, an athlete is likely to benefit if he is able to train and compete more often with the best and learn from them. Being the only super star in a losing team may not be equally satisfying as being among the middle-class in the world’s best team. In addition, a team may benefit more than the new team member’s individual skill set might suggest, if there are benefits arising from complementary skills between the team members. The audience may also enjoy the following sports events even more when they see more exiting matches or their favorite team becomes more successful. Of course, such changes come at the expense of other teams losing and some athletes not being able to play in the vest teams. Therefore, these externalities would have to be smaller than the added benefits, if we are to claim the change as beneficial as a whole. But in any case I would not claim that athletes changing nationalities and countries going for foreign athletes in hopes of more success in sports is wrong or necessarily counter-productive.

The idea of talented people moving abroad to improve their quality of life is discussed in the newspapers every now and then. Countries have to stay competitive, i.e. offer their citizens the possibilities for a good life, in order to avoid too many talented people moving abroad. If too many move abroad, a country’s capability to offer good opportunities to future generations gets undermined, as the current generation has less talent at its disposal. Another question is, how prevalent such changes are. If most people stay in their original home country, the flow of people between countries should not excessively undermine any country’s future. Quite the contrary, like with international trade, people moving abroad is likely to be beneficial because talents meet, get pooled and are able to combine their efforts more effectively and efficiently. As discussed before, some countries may also have different preferences for different goods and different capabilities for producing those goods. Therefore athletes, and people in general, moving between countries to maximize their potential may not be just acceptable, but also recommendable, for the benefit of individuals and a nation.

## Drift in politics – policies and voter opinions

Last week I finished the Coursera course on Model Thinking and among the final lesson were discussed the basics of game theory. Game theory was no new topic to me. I believe many have at least heard of it, but really applying it was an advancement. Finding the topic interesting, I dug a bit deeper and found a web course on game theory from Yale consisting of Youtube videos accompanied by transcripts and training material.

Median voter theorem

The third video lecture of the Yale course introduces the median voter theorem that roughly states that under certain conditions, politicians will tend to drift towards the political center in their opinions and supported policies. This drift is eventually their best response when they iteratively analyze their own and their opponents’ possible strategies. The theorem also implies that the media voter holds the decisive vote and, consequently, gets his will. The required conditions for the median voter theorem to hold are that the voters are symmetrically distributed on both sides of the centrist policies, the voters have so called single-peaked preference functions and there are a relatively small number of candidates competing for votes. For a large number of candidates a single extremist could get more votes than any of the dozen others fighting against each other at the the crowded political center. In addition, the median voter would not cast the decisive vote.

A short introductory article on the median voter theorem is offered by the University of Oregon. The theorem has its limitations, but even in its most basic form it offers a good start for analyzing election results, policy options and motives for implementing policies.

Median voter theorem in parliamentary politics

The median voter theorem (the concept was introduced by Harold Hotelling already in 1929) is relatively simple, but, as mentioned in the article from the University or Oregon, has interesting practical implications.  Already some years before the financial crisis of 2008, political parties with more extreme agenda were gaining on popularity and visibility.  A good example of this is the surge of the Finns Party in Finland, as illustrated by the graphic below. (The graphic is based on data from Statistics Finland. Only the largest parties having seats in the Finnish parliament are represented, covering at least 97% of the votes cast each year.)

According to the median voter theorem, there’s a third explanation. Since the theorem states that, under the assumptions (which I expect to hold reasonably well here), the decisive vote comes from the median voter, the Finns Party must have come closer in its policies to the three large parties or the median voter’s opinions had drifted towards the Finns Party. As the Finns Party profiled itself as a critic of EU-driven legislation, relatively free immigration and a supporter of conservative family values, being clearly apart from the three larger parties, the latter explanation seems more plausible. This is also supported by the fact that, based on the view one gets from the newspaper headlines today, SDP, KESK and KOK have drifted towards the Finns Party when it comes to EU and immigration, likely to redeem some of their lost voters. Especially the current crisis in the Middle-East and the following waves of refugees have made the leaders of the other large parties less eager to promote relatively free immigration and the on the EU level proposed refugee quotas per member country.

Drifting parties and voters

The median voter theorem offers two interesting observations. One, parties and politicians tend to drift towards one another, since the decisive vote is cast by the median voter, not by the one lying nearer to the extremes of the political spectrum and in any case voting for the party nearest to his opinions. Second, the ideological political center may drift, and parties previously positioned at the center may find themselves suddenly farther away from it, as may have been the case in the Finnish parliamentary election of 2011.

By the end of the year 2015, the Finns Party had lost almost 50% of its support after the parliamentary election in the Spring of 2015, being just below 10% in November 2015. This might be explained, as discussed in the article behind the link, by the unpopular decisions the Finns Party has had to accept as compromises between the parties in the government. This may have lead their immigrant critical supporters move to other parties, since the Finns Party’s stance does not differ that much from the other large parties and is milder than that of some other parties not represented in the Finnish parliament. Thus, by accepting policies that are ideologically positioned between them and the other governmental parties, the Finns Party may have drifted, at least in the eyes of their former voters, farther away from the current political center and closer to the other large parties. This drift may have cost them many voters who have turned to more extremely positioned parties. At the same time the Finns Party is competing for votes with the other large parties due to the four having drifted closer to one another. This makes life more difficult for all four parties since there are more takers for the same votes.

## Skill or luck – on outcomes, rewards and fairness 2/2

Who gets the prize?

In my previous post I showed how skill and luck play a role in most activities and why it is important to distinguish between the two and their impact on outcomes. I also argued that evaluating outcomes and awarding people only on that basis is not always right. Yet, we often evaluate outcomes, since they are often easy to grasp and measure. However, as already mentioned, if an individual’s or organization’s impact on a specific outcome is negligible in comparison to the impact that luck has, evaluation solely based on outcome is not fair. The individual should rather be evaluated based on his adhering to the agreed process used to reach the outcome, as previously discussed. Also, among top performers luck, paradoxically, plays a relatively larger role in deciding outcomes. Therefore, we should in evaluating performance and providing merit pay attention to the three following points:

1. Level of personal influence
2. The process used to reach the outcome
3. Level of competition

If we have no or very little personal influence on our success or failure, we should not be overly rewarded for good outcomes, nor punished or left completely unrewarded when the outcomes are less favorable. As mentioned before, luck dominated events might be shoved towards the skill dominated end of the spectrum, but this requires honing our skills and executing the event so as to maximize our impact. In this case, even if luck still dominates the outcome, we will have done our best to tilt the scales to our benefit; had we not followed the optimal process, the outcome would have been even worse. This implies that the correct process of working towards a goal and becoming proficient in that process should be merited, although measuring this might be more complicated than simply observing the outcome.

Finally, we should always observe the level of competition. If a person finishes last in the hundred meter dash finals in the Olympics, he is not a failure in sports and hardly beaten by the casual sprinter. Since luck has a larger role in defining the exact outcome at the top level, especially here we should give rewards for effort and process, not for the outcome. Of course outcomes do matter and they should be given merit. After all, if an outcome gets no merit, why would anyone go through the process required to reach that outcome? We just have to pay attention to the division of merit: as the pressure of reaching good outcomes and the desire for the prize get too high, the correct process may not be adhered to anymore, making the achieved outcomes also questionable.

Bonus or layoff, either way deserved?

As a practical example on rewarding individuals in a group of top performers I raise the rank and yank used by some companies to encourage their employees for better performance. The purposefulness of this policy is easily evaluated with the skill-luck model.

With rank and yank I refer to the practice where employees are annually ranked into multiple categories with fixed percentage quotas, and their future career development and remuneration is category dependent. For example, 10% are evaluated as top performers and they are given above average bonuses and promoted to more demanding position, 80% are average and receive the average bonus while keeping their current job and 10% are below average and have to be fired. Here we have at least three problems: role of skill and luck in an outcome, paradox of skill and the correctness of the evaluation. I will disregard the correctness of evaluation from further discussion, since it is a separate topic, but it is obvious that if the results of an evaluation are not correct or are inconsistent with other evaluations, any decision based on that becomes questionable.

As mentioned before, if the outcome of an individual’s work is largely dominated by luck, firing that individual due to poor outcomes hardly seems justified, assuming that the individual has tried to maximize the potential outcome to the best of his abilities. Also, if the individual belongs to a group of talented individuals, luck is bound to have a larger effect on the exact individual performance inside the group, again making the following gratification and firing of employees questionable.

Companies are reviewing and changing their evaluation and reward systems to help their employees learn and improve their skills constantly. For example, General Electric is using an mobile application that enables the supervisor to encourage and give positive feedback for  positive actions while asking to consider changing less desired ones. Here we see how placing the work process under focus might be the way how personal performance is evaluated and remunerated in the future.

Ain’t I lucky being so skillful

As a final thought a few words on the division of well-being on the global level since, here again, it is a question of skill and luck.

Nobody can choose the family and society to which they are born, nor can a person choose the time to which he is born. Yet, based on family ties and structure of the society, the easily accessible life and career paths are limited. A society offering good healthcare, public education for all and a stable government is much more likely to bring about successful individuals than a society plagued with high child mortality, low level of education and turbulent politics. Against this background, it makes me think what is the obligation of the richer countries to assist the poorer ones to reach higher standards of living? What is our obligation as individuals living in the richer countries to help those living in the poorer ones?

If my success is mostly dictated by luck, by having been born in the right country at a good time to the right parents, how much of the ensuing well-being belongs to me and how much should I share with others? I might claim that my success in studies and at work are a result of my own efforts, but they are also based on both nature and nurture, on my education (broadly understood) and genes, both of which are outside factors, or luck. This notion contradicts the definition of skill in the beginning of part one of this post, where I defined DNA and level of proficiency attained through education and practice to be individual attributes. As it seems, drawing a line between personal attributes and external factors is not easy. This makes the final distinction between skill and luck less clear, giving all the more reason for us to think about it and try to reach a fair solution.

## Skill or luck – on outcomes, rewards and fairness 1/2

Coming towards the end of my Coursera course on model thinking, I was introduced to the concepts of random walks and skill-luck model. Especially the skill-luck model appealed to me as it can be used to explain success on a personal and organizational level and predict, if success is due to skill or luck and if success is lasting. The following is based on the Coursera course Model Thinking by Scott E. Page and the course readings, mainly on How to Entangle Skill and Luck from Michael Mauboussin at Legg Mason Capital management from July 15th 2010. I have split my text into two parts to make the individual posts shorter.

The skill-luck model

The skill-luck model states that an outcome is based, with varying degree, on both skill and luck. Here skill denotes the knowledge and ability of an individual or organization to steer the future events in to the desired direction. Luck, on the other hand, incorporates the noise, random effects, that affect the outcome and cannot be controlled by the individuals or the organization.

To make the definitions more concrete we could say that the one hundred meter dash is mostly skill based, as the winner is based on the speed of the individual, and the speed is mostly dependent on strength, running technique, reaction time and other things that are either inherited in the DNA or a result of hard training and therefore dependent on the individual.

An example of a pure luck event is lottery. One cannot practice or have since birth any advantage that could help in choosing a winning number (clairvoyance excluded). The winning number is solely based on chance, or luck, as people often say.

A general formulation for the skill-luck model, presented also at the Coursera course by Mr. Page, is

Outcome = A*Luck + (1-A)*Skill

where A is constant between zero and one. The formula shows that, depending on the event, luck or skill may dominate, or they may be of roughly equal importance.

Why use the skill-luck model?

The skill-luck model has relevance on both personal and organizational level. In the society, most people arguably want to be successful, and so do organizations, composed of those very people. Some end up being successful, some not. Sometimes success is lasting; sometimes it barely greets us before already taking part.

Success is often looked up to and merited, while failure may be frowned upon or even punishable. Yet, if success or failure is based more on luck than skill, we should be careful in giving praise and delivering punishment. If success and failure take place randomly, it would imply that the accompanied fortunes and fame are provided without, or due to little, personal merit.

Identifying whether something is luck or skill dominated serves at least five purposes.

1. Ability to assess outcomes.
2. Anticipating outcomes and regression to the mean.
3. Giving guidance where we are most likely to be misled.
4. Fair evaluation and appraisal, which also promote learning.
5. More optimal resource distribution.

Assessing outcomes

With the skill-luck model we can assess, whether something is based on skill or luck. A good rule of thumb is, that you cannot lose on purpose in an activity that is dominated by luck, or at least losing on purpose is very difficult. An indicator of a skill dominated activity are lasting streaks. If a person consistently beats others and provides well above average performance consistently, providing that the observed sample is statistically representative, the event is likely to be skill dominated. Not all skilled people have streaks of success, but most streaks are done by skillful people, since the probability of streaks by chance is so low. A good example of a long-lasting streak is the already mentioned hundred meter dash, which has been dominated by Usain Bolt since 2008.

Another method for evaluating the role of skill and luck is to establish the base rate and compare it against actual observations. For example, when examining the role of skill in winning sport matches, the base rate would be the equivalent of a coin toss experiment, when the events consist of teams or individuals going one-on-one. If the group’s variance in the observed performance (for example percentage of games won) is much larger than the variance of the coin toss alternative (winning a game has a 50/50 chance), some contestants do consistently better than odds would have it, and so skill plays a relatively large role in the event. Yet, streaks and clusters can also be random. For example, if we throw a coin long enough, we would expect to get 20 heads in a row. The difference between luck and skill is also in the frequency of such streaks, which are achieved more often by skilled individuals, although they might be helped by some luck to keep the streak going on.

Here, in an MS Excel file,  is an example of a 6-game league between four teams (the method is described by Mauboussin in his paper). Each team plays 2 games against every other team. 1 in the table in the Excel file means that a team won the specific game, 0 indicates the losing team. As we can see from the calculations, skill would seem to play a large role in this specific game, where team 1 has been unbeatable. To ascertain such results in real life, large enough samples (also temporally) have to be ensured, which is not the case with this example, but it illustrates the point.

Anticipating outcomes and regression to the mean

After having identified the role of luck and skill in a specific event, we are more ready to anticipate outcomes of events. If an event is skill dominated, the most skillful are going to man the top positions. If the event is dominated by luck, anyone could win and predicting the top performers, not to mention the winner, becomes difficult. In a skill dominant event it is reasonable to expect that the most skillful will be the best performers, while the consistency of top performance is an indicator of a skill dominant event. This notion is not circular logic, rather it states that first we have to observe, if an event is skill dominant, as we have done in the previous paragraph. After enough observations have been done and the role of skill determined, we can predict, that in skill dominant events current success should be followed by future success, even if we have only few observations from individual performance.

The dominance of luck or skill has interesting consequences for anticipating outcomes. If an event is dominated by skill, it is quite certain that the few best will always be at the top, since the effect of random events, or luck, is so small. However, it is not certain that the absolutely best will win. Since the best can be very close to another in their skillfulness, the outcome is dominated by luck, by the small variations during the event and their effect on personal performance. Therefore, the top three or top five may consist of the same individuals from one event to another, yet the winner may never be the one with the most skill. This is called the paradox of skill. A further implication is that it is not always possible to find the best or most skillful, only the winner of a single event. If we cannot remove the effect of luck completely, small random effects make it difficult to distinguish the differences between individuals, when they are nearly equally skilled. The table below illustrates the paradox of skill. Player 1 is the most skilled, but due to small differences in skill, the least skilled Player 3 wins the game.

If an event is dominated by luck, it expresses the statistical property known as mean reversion: after an extreme event the next event is likely to be closer to the mean. This implies that extremely high or low values are often followed by mediocre results, which are in general more likely to take place. This also implies that if well above average performance does not regress to the mean or does so very slowly, an event is skill dominant.

To understand how regression to the mean can take place within groups while the variance of results in the whole population (consisting of those groups) stays the same, I encourage you to read pages 16 – 19 in Mr. Mauboussin’s paper.

Guidance to prevent us from being mislead

Not seldom are we inclined to draw conclusions from too small samples. For example, if an event is dominated by luck, we might nevertheless attribute the success of individuals to higher than average skill, although the outcome was dominated by luck. Therefore it is important to distinguish between skill and luck dominant events and also ascertain, what kind of tests are required to reach a solid conclusion.

Fair appraisal and evaluation and promoting learning

The roles that skill and luck play determine fair assessment and appraisal. If we are praised or punished for events that occur due to luck, the consequences are unlikely to be seen fair, eventually even morally wrong. An interesting point is that in some cases people are conditioned to being rewarded for giving bad feedback and going unrewarded for giving good feedback. This leads to restraining from praising a good performance, be it due to skills or luck, and calling errors in to attention, be they due to skill or luck. See Daniel Kahneman’s observation in Wikipedia for more information.

Mauboussin states in his paper, quite right in my opinion, that when luck is dominating an event, we should praise people for sticking to a prescribed process and becoming more proficient in the process and its execution. Only this way do we learn, by deliberately sticking to a process, repeating it and honing it. That is a time consuming process and not always pleasant or easy. However, this repetition improves our skills and reduces the role of luck in the considered event, making it more skill based. Therefore we should, as the cliché often goes, praise and give prize for hard work and effort, not necessarily for the good outcome.

Optimal resource allocation

If we know an event to be dominated by skill, we can improve the outcome by allocating more to the disposal of the most skillful ones, assuming the they still have excess capacity to use those resources. For example, two factories produce similar goods, but the other one has a more advanced technology that leads to lower production costs. However, this factory does not have enough capital to invest into more production capacity that is needed in any case to produce all the demanded goods. We might reduce the funding (bank loans for investments into new equipment) to the other factory and use it to increase the capacity in the more efficient one, thus reducing total average production costs while increasing capacity. If both factories would be efficient one day and completely inefficient the other, production thus being a luck dominated effect, such re-allocation of capital would not make sense.

Like in the case of randomly efficient factories, we should not take a bank loan and ask the last week’s lottery winner to play with the whole sum. As lottery is a pure game of luck, investing in a specific individual does not increase the chance of success.

Edit 10.9.2016: Corrected typos.

## Use your tools, lest they rust away

During the Coursera course on model thinking I have learned the basic principles of many models, ranging from segregation over economical models to military strategy. I have learned how simple can models can give insights into many everyday problems and phenomena, when you know the correct models and can apply them. And that is the difficult part.

Like with any tools, models are only useful when they are used at the right time for the right purpose, and in order to do that they have to be available, applicable and the user has to be proficient in using them. It’s not unlike with kitchen knives. They are only useful when you have the correct knife available, it is sharp and you are proficient in using it.

In order to improve my modeling abilities and use my newly acquired toolset I will try to ask myself more often, which model I could use to analyze a problem or a phenomenon. Currently the newspapers are almost daily offering reports about the refugee crisis in the Middle-East and Europe. I could imagine doing some simple analyses using the segregation model to analyze, when and why domestic people might move inside a country when refugees arrive from abroad. Or I might use a simple demand and supply model, combined with an oligopolistic market model to analyze what the effect of the current oil price on the Russian economy will be in the long term, if the price even will stay low for an extended period of time.

Now I have my set of knives before me. It’s up to me to learn how to use them, keep them sharp and wield them when they can help me slice a problem into more digestible pieces.