Playing mixed strategies with Leo Messi

Playing a mixed strategy means in game theory choosing a probability distribution between two or more available actions (or pure strategies). For example, tossing a coin to decide whether to kick to the left or to the right, is one possible choice of a mixed strategy. In the real world, we don’t take many decisions literally like this. But some interactions have been found were actors decide as if choosing mixed strategies. One that is easily amenable to empirical work is penalty kicks in soccer. Economist Palacios-Huerta and psychologist Bar-Eli, separately, have found that both kickers and goal-keepers behave as if choosing rationally their mixed strategies (not literally, because they do not toss coins or other random devices, but mentally, intuitively).

As a result of Leo Messi missing a few important penalties recently, there is a debate about his suitability to the job of kicking penalties. But data shows that he behaves optimally, as predicted by scholars: mostly shooting to his natural side, sometimes to the other, missing around 20% of penalties and achieving a similar success ratio when kicking to the right or to the left (otherwise there would be one clear best strategy, and he would be predictable). That means that he is probably rational and optimal.

It s also true that he may illustrate another feature uncovered by behavioural sciences: choking under pressure. His success ratio decreases dramatically when he kicks crucial penalties (at the end of games most notably).

Messi is an average penalty kicker. Should he be replaced in that role? Probably if another player kicked the same number of penalties he would also score around 80% like Messi, although perhaps doing better in the last minutes of games. But no manager in the world will tell the best player not to kick a penalty if he wishes. Should he think more about how to kick penalties? Should he have a penalty coach, a full time employee working on that with him? That would interfere with his natural decision making process, which is intuitive and unconscious. That is his way of being rational.

I was almost wrong in November 2013 when I wrote a post suggesting to sell Messi (well, just playing with the idea): he did better in the World Cup with Argentina than I expected (although as I expected Argentina did not win, and his winning the trophy to the best player was controversial), and this season he is in much better shape so far than I expected (better than in the World Cup). But does that mean that I am not wrong or that I am still right? That is, perhaps since he is still so valuable it is still time to sell him NOW because a lot of money can be made that can be used to maximize the long run probability of winning games and titles. He is better than I expected, but he is not better than he was in 2008-2011, and he will not get much better than that (in other words, he is beyond his peak age). In penalty kicks he is certainly not better.

Since there is no clear option about selling him or not, perhaps the best way to decide about that is to randomize. And perhaps that is precisely what FC Barcelona are doing by replacing technical director Andoni Zubizarreta by a bicephalous body with the heads of two unpredictable agents: veteran former player Carles Rexach and former Berlusconi employee in AC Milan Ariedo Braida.

Three tier agency structures

In the simplest principal agent model, there is one principal, one agent, and one dimension of effort. The principal (for example an owner) tries to motivate the agent with monetary (extrinsic) incentives. In the real world, agency relationships can be much more complex than this. For example, in sports, managers and referees are in between higher principals and agents. The higher bodies are club officials, governing bodies and leagues, which define the institutional framework and the incentive structure of managers and referees, and determine the quality of their role as coordinators or rule-enforcers. Academics and teachers have a similar role: they are the principals for students, but they are agents of other principals themselves. Their performance depends on the institutional quality determined by the higher principals: the university or school authorities and rules. Managers, referees and teachers try to combine extrinsic and intrinsic incentives as well as they can. Intrinsic incentives are especially important when there are quality issues or other dimensions that are hard to measure but important nevertheless. Sometimes extrinsic incentives may crowd out intrinsic incentives, like when highly motivated students are asked to waste time answering a formal test. But sometimes extrinsic incentives complement intrinsic incentives, like when a league reforms the incentive system of referees, as it has been happening in European soccer leagues in the recent past. In institutions such as the education system, or even the financial system, where those who are in contact with the customers or users are agents themselves, the quality of these complex contractual structures are a key component of institutional quality. In this case, good institutions are those that give good extrinsic and intrinsic incentives to intermediate agents.

The gratitude is ours, Dr. Sacks

Without being my specialization at all, I have been a consistent reader of the books by Dr. Oliver Sacks, a neurologist and writer. His book chapters on individuals who experienced interesting phenomena in their mind (he writes as if the individuals were not victims of any illnesses, but of special circumstances) always gave me pause for thought and were great sources of entertainment. I remember knowing from his books about the Tourette syndrome (and reflecting that perhaps some of my acquaintances had it), or becoming amazed about people asking to get back to blindness because they could not cope with the sudden gift of vision. Now Oliver Sacks announces that his body will leave us soon. But what a productive life! Happily, he has several books down the road, including his autobiography. So, from the point of view of his readers, his real death is still very far away. This is part of his farewell article in the New York Times: "This is not indifference but detachment — I still care deeply about the Middle East, about global warming, about growing inequality, but these are no longer my business; they belong to the future. I rejoice when I meet gifted young people — even the one who biopsied and diagnosed my metastases. I feel the future is in good hands.

I have been increasingly conscious, for the last 10 years or so, of deaths among my contemporaries. My generation is on the way out, and each death I have felt as an abruption, a tearing away of part of myself. There will be no one like us when we are gone, but then there is no one like anyone else, ever. When people die, they cannot be replaced. They leave holes that cannot be filled, for it is the fate — the genetic and neural fate — of every human being to be a unique individual, to find his own path, to live his own life, to die his own death.

I cannot pretend I am without fear. But my predominant feeling is one of gratitude. I have loved and been loved; I have been given much and I have given something in return; I have read and traveled and thought and written. I have had an intercourse with the world, the special intercourse of writers and readers.

Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and adventure."

The best lectures

These days I am following an on-line course about “English for Teaching Purposes” and I was fortunate to come across TED from several different sources at more o less the same time. This is a platform of great talks that can be watched with on line videos. It seems to me that the four best of these are:

-This one on how statistics change, and how our beliefs about developing countries are dominated by prejudices, and also about the great diversity between countries and inside countries.

-This one about how knowledge is positively correlated with ignorance. Perhaps it can be summarized as knowledge leads people to a better ignorance: the more we know, the better questions we ask.  

-This one, on how our intelligence has adapted to technological changes, and how we have evolved from thinking about the concrete to thinking about the hypothetical. 

-This one about bad science, and how fads are propagated and the difficulties of protecting people from interested lies.

All these speakers have very different styles, but all of them are great communicators. Above all, it shows that reason and science are not incompatible with emotion and excitement, In the web page, there are many other talks, so I’m sure that you will also find your own favourite video.

The answer of Piketty to Acemoglu and Robinson

Thomas Piketty has published in the Journal of Economic Perspectives his own views on some of the debates that have emerged as a result of the success of his book, "Capital in the XXI Century." One of these debates has to do with the role of institutions in economic history. Acemoglu and Robinson, the authors of "Why Nations Fail" had argued that the book by Piketty neglected the role of institutions. I already wrote previously that this criticism was very surprising, because to me the French economist does precisely the opposite: institutions are a key determinant of the degree of inequality in his approach, and also a key component of possible remedies to alleviating inequality. Here is what Piketty has to say:
"However I believe that our approaches are broadly consistent and complementary to one another: they differ in terms of specific institutional content, as well as in time and geographical scope, more than in substance. In some of their earlier work, Acemoglu and Robinson mostly focused upon a relatively specific institution, namely the protection of property rights. In their fascinating book Why Nations Fail, they develop a broader view of institutions and stress the distinction between “inclusive” and “extractive” institutions. This broad concept might certainly include the type of institutions and policies on which I focus upon, including progressive taxation of income, wealth, and inheritance, or the modern welfare state. I must confess, however, that seeking to categorize institutions with broad terms like these strikes me as maybe a little too abstract, imprecise, and ahistorical. I believe that institutions like the welfare state, free education, or progressive taxation, or the effects of World War I, the Bolshevik revolution, or World War II on inequality dynamics and institutional change, each need to be analyzed in a precise and concrete manner within the historical, social, and political context in which they develop. While Acemoglu and Robinson (2012) in their earlier book take a very long-run perspective on the history of the planet (from prehistoric times to the “great discoveries” and the formation of the modern world), I tend to focus on the historical periods and countries on which I was able to collect systematic data, that is, on the 18th, 19th, and especially the 20th centuries (an important period indeed for the formation of the modern social and fiscal state)."

The solution to Greece: a federal Europe

Many observers have been arguing that the tension between the new Greek government and the European leaders should be solved in the direction of a new federal agreement that not only reaches a compromise for the Greek, but also amounts to a review of the Brussels institutions. As Eugenio Scalfari argues today in La Repubblica, the significance of this request is likely a step to the federated Union rather than the Confederate current one, with its transfers of sovereignty from the member States. This seems the more positive among those Tsipras hopes to achieve; it is not just about Greece and should be the objective of the whole Union. Unfortunately it is not, at least as yet, but it is however and paradoxically the objective of the European Central Bank. It may seem paradoxical also that the boost to the United States of Europe comes from a country that is on the brink of a precipice, and even in the streets shouting their despair. It could be put in a position to leave the euro and asks not only for flexibility and aid money but even the birth of a State which is called Europe and has the powers hitherto scattered over 28 countries. If in this point there is coincidence between Tsipras and Draghi, also the fulfillment of economic commitments of Greece would become easier. But opponents are many, indeed all national governments do not want to lose their sovereignty. Until they see that they have no other option.

Re-balancing democratic federalism: the example of soccer

This week I discussed with my students (in the course on the economics of soccer that I teach at the Study Abroad program at UAB) the article by Branko Milanovic "Globalization and Goals." The article has three parts. In the first part, the author presents a simple theoretical model where the introduction of free trade of players among clubs increases the concentration of talent (because the richest clubs get the best players), increases average quality (because of the multiplicative nature of the production function among players), and increases equality among national teams. This is so because quality is endogenous, and the best players from even the poorest countries go to play in the best leagues. In the second part, he presents evidence consistent with these trends from the European Champions League, the Italian League and the World Cup. And finally he compares these trends with trends in general in the global economy. He claims that global soccer is an example where free trade increases efficiency, but this efficiency is compatible with redistribution because of the presence of institutions, in this case the rules of global soccer enforced by a true global authority, FIFA. According to these rules, mobility of players at the club level is not matched at the national level, where players can only play for one national team all their life. An obvious example is The Netherlands: before the Bosman ruling Ajax Amsterdam were among the likely winners of the top European competitions, but now they are no longer so because the best players go to richer leagues at a young age. However, the Dutch national team is still very competitive, because these same players reunite in summer to play national team competitions. The argument is that if we had a similar institution in the global economy we could make efficiency compatible with redistribution. I agree, with the caveat that one must make sure that this institution avoids the opacity and apparent corruption of FIFA. Even though soccer is very democratic (one could argue, too democratic and populist) at the local level, it becomes too distant from democratic rules at the global level. FIFA is more a powerful and distant body than a democratic federal body. Perhaps it is time to introduce more constraints to direct democracy at the local level (managers would appreciate it) and create more constraints at the global level, so that FIFA preserves its welfare enhancing powers but eliminating the corruption temptations. The details of all this are obviously to be filled in.