Sunday, 24 May 2015

In memoriam: John Nash

It is with great sorrow to report the news that one of the greatest minds in human history died yesterday in a car crash with his wife while they were returning home from an airport. John Forbes Nash Jr., to most widely known as one of the founders of cooperative game theory whose life story was captured by the 2001 film "A Beautiful Mind", is truly one of the greatest mathematicians of all time. His contributions in the field of game theory revolutionized the way we think about economics today, in addition to a whole number of fields - from evolutionary biology to mathematics, from computer science to political science. 


John Nash was born in 1928 in Bluefield, West Virgina. Even as a child he showed great potential and was taking advanced math courses in a local community college on his final year of high school. In 1945 he enrolled an undergraduate mathematics major at the Carnegie Institute of Technology (today Carnegie Mellon). He graduated in 1948 obtaining both a B.S. and an M.S. in mathematics and continued onto a PhD at the Department of Mathematics at Princeton University. There's a famous anecdote from that time where his CIT professor Richard Duffin wrote him a letter of recommendation containing a single sentence: "This man is a genius". Even though he got accepted into Harvard as well, he got a full scholarship from Princeton which convinced him that Princeton valued him more. 

While at Princeton, already on his first year (in 1949) he finished a paper called "Equilibrium Points in n-Person Games" (it's a single-page paper!) that got published in the Proceedings of the National Academy of Sciences (in January 1950). The next year he completed his PhD thesis entitled "Non-Cooperative Games", 28 pages in length, where he introduced the equilibrium notion that we now know as the Nash equilibrium, and for which he will be awarded the Nobel prize 34 years later. It took him only 18 months to get a PhD! He was 22 at the time. 

While at Princeton he finished another seminal paper "The Bargaining Problem" (published in Econometrica in April 1950), the idea for which he got from an undergraduate elective course he took back at CIT. It was Oskar Morgenstern (the co-founder of game theory and the co-author of the von Neumann & Morgenstern (1944) Theory of Games and Economic Behavior) who convinced him to publish that bargaining paper. The finding from this paper will later be known as the Nash bargaining solution. Princeton was full of top academics at the time and Nash took full advantage of that, even though he didn't learn maths by attending classes, he did it by trying out his own ideas. As he came to Princeton he sought out Albert Einstein to discuss physics with him (as physics was also one of his interests). Einstein reportedly told him that he should study physics after Nash presented his ideas on gravity, friction and radiation. 

Illness and impact

After graduating he took an academic position at MIT, also in the Department of Mathematics, while simultaneously taking a consultant position at a cold war think tank, the RAND Corporation. He continued to publish remarkable papers (his PhD thesis in The Annals of Mathematics in 1951, another paper called "Two-Person Cooperative Games" in Econometrica in 1953, along with a few math papers). He was given a tenure position at MIT in 1958 (at the age of 30), while he married his wife Alicia the year before. However, things started to go wrong from that point on in his personal life and career. In 1959 he was diagnosed with paranoid schizophrenia, forcing him to resign from MIT. He spent the next decade in and out of mental hospitals. Even though he and his wife divorced in 1963, she took him in to live with her after his final hospital discharge in 1970. 

Nash spent the next two decades in relative obscurity, but his work was becoming more and more prominent. Textbooks and journal articles using and applying the Nash equilibrium concept were flying out during that period, while most scholars that built upon his work thought he was dead. It was not only the filed of economics - where the concepts of game theory were crucial in developing the theory of industrial organizations, the public choice school and the field of experimental economics (among many other applications) - it was a whole range of fields; biology, mathematics, political science, international relations, philosophy, sociology, computer science, etc. The applications went far beyond the academia; governments started auctioning public goods at the advice of game theorists, business schools used it to teach management strategies. 

Arguably the most famous applications were to the cold war games of deterrence that explain to us why the US and Russia kept on building more and more weapons. The Nash equilibrium concept explains it very simply - it all comes down to a credible threat. If Russia attacks the US it must know that the US will retaliate. And if it does, it will most likely retaliate with the same fire-power Russia has. Which will lead to mutual destruction of both countries. In order to prevent a full-scale nuclear war (i.e. in order to prevent the other country from attacking), the optimal strategy for both countries is to build up as much nuclear weapons as they can to signal to the other player what they're capable of. This will prevent the other player from attacking. If they are both rational (i.e. if they want to avoid a nuclear war and total destruction) they will both play the same strategy and no one will attack. Paradoxically, peace was actually a Nash equilibrium of the arms race!

Long-overdue recognition 

Little did Nash have from all this. He had no income, no University affiliation and hardly any recognition for his work (not counting the citations). But this all changed in the 1990s when he was finally awarded an overdue Nobel Prize in Economics in 1994, with fellow game theorists John Harsanyi and Reinhard Selten "for their pioneering analysis of equilibria in the theory of non-cooperative games". Here is the Nobel Prize lecture and here is an interview with him conducted 10 years after winning the prize. 

His remarkable and actually very painful life story was perfectly depicted by his autobiographer and journalist Sylvia Nasar in her two books; "A Beautiful Mind", based on which the movie was made, and an even better one "The Essential John Nash", which she co-edited with Nash's friend from college Harold Kuhn (also a renowned mathematician). As Chris Giles from the FT said in his praise of the book: "If you want to see a sugary Hollywood depiction of John Nash's life, go to the cinema. Afterwards, if you are curious about his insights, pick up a new book that explains his work and reprints his most famous papers. It is just as amazing as his personal story." The book contains a facsimile of his original PhD thesis, along with eight of his most important papers (from game theory and mathematics) reprinted. 

After the Nobel Prize success things got better for Nash. By 1995 he recovered completely from his "dream-like delusional hypotheses", stating that he was "thinking rationally again in the style that is characteristic of scientists." Refusing medical treatment since his last hospital intake, he claimed to have beaten his delusions by gradually, intellectually rejecting their influence over him. He rejected the politically-oriented thinking as "a hopeless waste of intellectual effort". He remarried his wife Alicia in 2001, and started teaching again at Princeton. He continued his work in advanced game theory and has moved to the fields of cosmology and gravitation

The Phantom of Fine Hall, as they used to call him in Princeton due to his mystique and the fact that he used to leave obscure math equations on blackboards in the middle of the night, will never cease to raise interest, praise and awe. Nash was another perfect example of a thin line between a genius and a madman. Luckily in the end the genius side prevailed.  

So what is the Nash equilibrium? 

The reason why this concept was so revolutionary was because it significantly widened the scope of game theory at the time. In the beginning, following the von Neuman and Morgenstern setting, game theory was focused mostly on competitive games (when the players' interests are strictly opposed one to another). These types of games were known as zero-sum games, limiting to a significant extent the power of game theory. Nash changed that by introducing his solution concept so that basically any strategic interaction between two or more individuals can be modeled using game theory, where the most unique solution concept is the Nash equilibrium. Games are not zero-sum, they aren't pure cooperation nor pure competition. They are a mixture of both. 

The idea of the Nash equilibrium resonates from the simple assumption of rationality in economics. The term rationality in economics is not the same as common sense rationality we all think about upon hearing this term. It refers to the idea that each individual will act to achieve his or her own objective (maximize their utility), with respect to the information the person has at his/her disposal. The concept of rationality in economics is therefore idiosyncratic - it depends on whatever a particular individual deems rational for themselves at a given point of time. It rests upon the idea that a person will never apply an action that hurts him/her in any way (lowers his/her utility). 

The Nash equilibrium is the most general application of this idea. A non-cooperative game, according to Nash, is "a configuration of strategies, such that no player acting on his own can change his strategy to achieve a better outcome for himself". In other words if there exists another strategy that can make an at least one individual better off, then the outcome does not satisfy the condition for a Nash equilibrium. 

Let's look at an example. The most simplified example of how a Nash equilibrium solution concept works is the Prisoner's Dilemma game. Consider two robbers arrested for a crime. They are both being interrogated by the police in separate rooms. They are presented with two options (strategies): keep quiet (silent) or betray the other guy (betray). If they both remain silent, they both only get a light sentence of a year in prison for obstructing justice. If one betrays the other, and the other guy keeps silent, then the betrayer is released with zero imprisonment, and the other guy gets pinned for the whole crime and gets nine years in prison. If they both betray each other, they both get six years in prison. What's the optimal thing to do?

Applying the Nash equilibrium concept we need to find a strategy that is the best response of one player to whatever the other player may decide. When no players have any incentive to deviate from a set of strategies (strategies are always a pair in two-person games) we can say that this set of strategies is a Nash equilibrium. 

Consider the game depicted in the table below:

Prisoner 2
Silent (cooperate)
Betray (defect)
Prisoner 1
Silent (cooperate)
-1,-1
-9,0
Betray (defect)
0,-9
-6,-6 *

It would seem that the best strategy they can apply is for both to keep silent. If they do, they both get only a light sentence. However this strategy set (-1,-1) is not a Nash equilibrium since at least one person has an incentive to deviate. In fact, they both do. If Prisoner 1 decides to defect and betray Prisoner 2, he gets 0 years in prison, while Prisoner 2 gets 9 years (third cell, with payoffs 0,-9). Prisoner 2 applies the exact same reasoning (second cell with payoffs -9,0). In the end since the better strategy is always to betray, they both play the same strategy (betray, betray) and end up with payoffs (-6,-6) which is the Nash equilibrium of this game. From this point no player can deviate and make himself better off. If Prisoner 1 decides to go for silent he risks getting 9 years in prison instead of 6. There is no way for them to reach a cooperative equilibrium in this simplified scenario.

Naturally, cooperative games do exist (as I've discussed earlier on this blog) and they help us understand how game theory solves for example the free rider and the collective action problem. It was Elinor Ostrom (1990) who applied these concepts to reach her optimal solutions in solving the common pool resource problem in small groups with persistent interactions. Robert Axelrod (1984) is another, finding that even though the defection strategy is more rational, sometimes various other factors will result in a cooperative outcome between the players. The Nash equilibrium helped initiate a huge amount of research on these and many other problems within and outside the academia. The reason game theory is usually considered as the most applicable economic theory - in that it can be used to solve real-life problems - is purely thanks to John Nash. 

Rest in peace. 

Most notable papers: 

Wednesday, 20 May 2015

Video: How would a Nobel prize winner run the economy?

From LSE's You Tube channel:

If the video doesn't work (some browsers could do that), see it here.

LSE's Nobel professor Christopher Pissarides is being 'grilled' by Conor Gearty in his Gearty Grillings. The short video surprisingly includes a lot of good ideas on the size of state, labor markets, and the Eurozone troubles. Even though he declares him self an open social democrat, it's obvious he believes in the power institutions and doesn't succumb to any of the typical socialist fallacies. Nor is he being unrealistic about the solutions awaiting Europe. 

Just to remind the readers, Pissarides won the Nobel prize for his search frictions theory in the labor markets. Here's the Nobel prize lecture, and you can find some of his best papers here, and the newest ones here.

Friday, 15 May 2015

Eurozone challenges

Here's an excellent infographic from Boston University explaining in one place and with much detail why the crisis in Europe is still a long way from being over: 


Boston University Online

If I had to sum it up in words, it would go something like this: sluggish recovery, threat of deflation, high unemployment (11.2%), particularly youth unemployment (23%; the worst still in Spain = 51%), lack of access to finance for small businesses (banks are still hoarding cash), low productivity, low wage growth, an increasing threat of poverty, and of course - still huge levels of public debts (corporate and household as well), coupled with an ageing population which is a lethal combination for a sustainable pensions system, particularly to those countries who in addition to huge debts and an ageing population are experiencing net emigration (Spain, Greece and Italy are leading the way). 

So the overall picture is, unfortunately, still bleak, to say the least. At this moment I don't see how Europe is going to avoid being stuck in a Japanese-style decade-long stagnation. It's facing its own "balance sheet recession" as Richard Koo would call it. Japan however had one important caveat, it never faced a problem of high unemployment. Furthermore, if you reach a living standard as Japan has had in the 90s, then going through 20 years with close to zero growth is not that big of a problem. You're still a very rich country. However in Europe many of the Member States are not quite there yet. For most of them it's entirely their fault, but facing a decade or two of stagnation is not good news for a country yet to face the full benefits of EU convergence. 

Thursday, 30 April 2015

Immigration helps the natives

At some point in the middle of 2014, opinion polls in the UK revealed that immigration became the most important issue in Britain (see graph below), surpassing even the debates on the economy (probably because the economy is now in a better shape than before, with 2014 growth around 2.6%). What best showed this change in sentiment was the homepage of the British Office for National Statistics (ONS) during the autumn of 2014, where the first figure you could see was that of net migration (which was around 300,000 in 2014). During the 'good old times' of the stagnant recovery (2009-2013), the first thing you could see when you entered the ONS website were the GDP growth estimates, followed by numbers for the CPI, budget deficit, business investments, etc. For quite some time the main page didn't even feature data for the debt and deficit. You had to dig around to find them.

Obviously the Britons are bemused with the popularity of the UK Independence Party, particularly after their unprecedented triumph at the EU Parliament elections in May 2014. They are a party which was originally focused on a single goal - get Britain out of the EU. To that goal they have added a plea to "take back control of our borders", or in other words, limit immigration. And they've landed in a gold mine. As mentioned before, according to survey data, Brits consider immigration the most important issue facing Britain, overtaking even unemployment, NHS (always an important topic in Britain) or the economy. Notice how these issues correspond to varying historical periods. Back in the 80-ies and the 90-ies unemployment was the biggest issue, followed by the NHS and immigration in pre-crisis times, overtaken completely by the economy during the crisis and the recovery, until last year when immigration started gaining momentum. The recent opinion polls confirm this trend - immigration is still the hottest issue in the country, just a few weeks before the elections. 
Source: The Economist. Click to enlarge.
The Conservative government was quick to respond to these trends. But not for reasons one would immediately think of. The Conservatives were simply afraid of UKIP's growing popularity, afraid that in the national elections UKIP will take many of their own voters thus causing them to lose the elections to Labour (although these fears have receded lately, as the race became neck and neck, and as the Tories are looking to UKIP as partners in their new government). Two Tory MPs have already defected away from the party, gaining two seats for UKIP in Parliament (UKIP has never held seats in Parliament before). This only further increased their popularity and their presence in the media, where their ideas to curb immigration (among other things) are gaining more and more political clout.

As a response the PM David Cameron has announced a tougher stance on immigration, and has even promised an in-or-out EU referendum for Britain if elected as Prime Minister once again. He has also announced changes in restrictions on EU migrants as a point of further negotiation between UK and the EU, aiming to restrict even the EU incoming migrants. Under current EU laws this would be prohibited since it would violate the assumption of freedom of movement and equal status of all EU citizens. Which is exactly why UKIP is calling for an EU exit, stating that "Britons must leave the EU if they want to cut immigration." 

"They took 'r jobs!"

It's hard to tackle such an issue in purely economic terms. Politics has to be involved. You will hardly find an economist opposing immigration, just as you will hardly find an economist opposing free trade, or promoting rent control. However this doesn't prevent politics from imposing immigration restrictions or tariffs and quotas. All for the - supposed - protection of domestic jobs. But in economic terms it is fairly obvious that protection of jobs steaming from immigration restrictions causes much more problems than benefits. 

The anti-immigration argumentation suffers from the typical fallacy that the demand for work is limited so that by giving a job to one person means you're taking it from someone else. Even though this seems quite intuitive at first (higher supply simply implies the price going down if demand stays the same), the fact is that immigration doesn't just increase the supply of labor, it also increases the demand for labor, since immigrants earn salaries they spend in the city they reside. They pay rents, buy food, clothes, cars, houses. They add to the demand for other goods and services out there, thus increasing the overall demand for labor. The exact same thing happens when a young graduate enters the job market - they don't steal a job from anyone, they simply increase the demand for jobs. Firms expand, economies grow. More people can only be a good thing for an economy over the long run. Think about why countries facing depopulation are in big problems. Those facing net immigration surely aren't. At least in economic terms.  

An article in the New York Times sheds some evidence on this 'Lump of Labor' fallacy: 
"The single greatest bit of evidence disproving the Lump of Labor idea comes from research about the Mariel boatlift, a mass migration in 1980 that brought more than 125,000 Cubans to the United States. According to David Card, an economist at the University of California, Berkeley, roughly 45,000 of them were of working age and moved to Miami; in four months, the city’s labor supply increased by 7 percent. Card found that for people already working in Miami, this sudden influx had no measurable impact on wages or employment. His paper was the most important of a series of revolutionary studies that transformed how economists think about immigration. Before, standard economic models held that immigrants cause long-term benefits, but at the cost of short-term pain in the form of lower wages and greater unemployment for natives. But most economists now believe that Card’s findings were correct: Immigrants bring long-term benefits at no measurable short-term cost."
Political implications 

Economics isn't the only part of the equation. An even bigger concern about immigration than job losses for domestic workers are benefits being taken by immigrants. The usual accusation is: "they've contributed nothing but are taking away from the system". This is particularly troubling in Britain which has universally accessible health care and welfare services, which according to the prevalent opinion of the British population, tend to be overcrowded by immigrants.

A further issue is the problem of assimilation of immigrants. There can exist entire neighborhoods where no one even speaks the language of the country they're in. This is a problem both the US and Europe are increasingly facing. Many immigrants cluster in certain neighborhoods where apparently the same rules don't apply. By doing this they self-select themselves out of the domestic society and it becomes very hard for them to assimilate. Particularly for the first-generation immigrants. There is always an issue of respecting one's culture, but in some cases this may go too far where the minority fails to respect the culture of the host nation. As crime rates increase in such areas, that's when the issue truly becomes political. And then it's quite difficult to use economic reasoning to solve the immigration issue. No one wants to hear about the long term benefits of net immigration, or how they increase domestic productivity, if violence is escalating (just think of France). If the benefits are not immediate and quite obvious, no one really takes them into consideration. It's easier to make inferences on our immediate observations. After all, we have a tendency of highly discounting the future. 

However the most interesting thing about surveys of opinions about immigration is the location and the relative exposure to immigrants. For example in London, one of the most multicultural cities in the world, its citizens share the most liberal views about immigration. As you move further down the line, the less immigrants a constituency has, the more likely it will see immigration as a crucial issue. People like to exaggerate as well. In the same survey measuring sentiment towards immigration, the people were asked how many foreign-born immigrants are there in the UK. The answer on average was 31% of the population. The actual number is 13%.

In the next text I'll present some more evidence on immigration vis-a-vis job creation, labor market performance and education. 

Sunday, 19 April 2015

Graph of the week: Happy, happy Europe

From the Economist, calling upon a report from Eurostat: what drives happiness in Europe and how heterogeneous European countries tend to be when it comes to the satisfaction with their living standards. 

Source: The Economist
"ONE frequent stumbling block for the European project is the fact that different countries want different things. Recent Eurostat polling on self-reported happiness highlights those divergences. As usual, Scandinavians are the happiest people in Europe and retired Danish women are the cheeriest among them, reporting a happiness score of 8.5 out of 10. In general, geography is the best predictor of merriness, followed by pay. At all income levels a step up one quintile on the income scale makes people more content. Yet the poorest 20% of Danes are more joyful than the richest Greeks."
Bear in mind that the data on happiness is self-reported, which can make it a bit biased. However, even with all the problems of self-reported survey data, the story is quite clear and actually well-known: Scandinavian nations - the leaders in economic freedom rankings, competitiveness, doing business, and prosperity rankings - by far outweigh the rest. Their economic model is based first and foremost on efficiency. There's no ideology attached to it, only pragmatism. If something works, apply it. South European nations, namely Spain, Italy, Greece and Portugal, should take note. 

Notice another interesting fact; usually life in the South of Europe is portrayed as relaxed and easy-going, implying its people are quite content with their lives. Warm climate in the South must mean that its citizens are much happier than their Northern counterparts, consumed with heavy rains and cold weather. The data on happiness consistently fails to show this. Regardless of the effect of the crisis, Northerners were always much happier. Climate has nothing to do with it. The economy (read: institutions) does. 
Source: The Economist
"Where one lives within a country is also important. Around the Mediterranean people prefer towns, while near the Arctic Circle rural life is best. Procreation affects cheerfulness too. In southern Europe families with children are happiest, whereas the British and Irish are the only people to become sadder when little ones arrive. Ageing draws out differences. Everyone is happiest when young and less so in middle age. But in old age the British and Scandinavians cheer up while in the south retirement is a miserable affair. Debt crises and financial woes are not the only reason life within Europe is so often frowned upon."
The last part is the most interesting: "in old age the British and Scandinavians cheer up while in the south retirement is a miserable affair". The British and the Scandinavians (I would add the Germans as well) understand the value of life-long savings. Their institutional arrangements make it so. This is another crucial North-South European divide. The more care-free the citizens are at the start of their careers (see happiness in ages 16-24), the worse off they get when they are retired (notice the movement of the yellow circle across age groups in the second figure). Tough news for the youth unemployed of Spain, Greece, Italy and Portugal. Will they ever get to enjoy their lives? Or is this the beginning of a truly lost generation in Europe?