Penalty taking: some game theory and hypothesis testing

One of my colleagues sent me an article in the Financial Times from March 17 entitled “How to save a penalty: the truth about football’s toughest shot. On star goalie Diego Alves, game theory and the science of the spot kick.” I found the article interesting for two reasons.

  1. It has a fun discussion of the psychology and game theory of taking penalty kicks. It points to the paper by Ignacio Palacios-Huerta in which he shows that professional soccer players take penalties in a way that is consistent with Nash equilibrium (or minmax) behavior. The FT article also includes an interesting interview with Ignacio Palacios-Huerta and his “analysis of ideal penalty-taking strategies for the then Chelsea manager Avram Grant before the Champions League final against Manchester United in 2008.”
  2. The FT article highlights Diego Alves, Valencia’s goalkeeper, and argues that he is particularly good at stopping penalties. The FT article argues that Diego Alves’ stopping record (he stopped 22 of 46 penalties – a very high number compared to the average stopping rate of 25% of all goalkeepers combined) cannot be explained by chance alone.

In this blog post I want to comment on the 2nd point. It is actually wrong. And it is wrong for an interesting reason. Moreover the mistake made is very easy to make and is a very common one.

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Three thoughts on free trade

The Wachau is a roughly 40km long and narrow part of the Danube valley in Austria. It produces and sells essentially only three things: beauty, wine, and apricots. With “producing and selling beauty” I mean that it tries to and manages to attract tourists. Its wine-growing and trading goes back a long way.

Except for perhaps in pre-historic times, it seems that the Wachau was never autarkic, meaning there was always trade (and probably also migration) between the Wachau and the world around it.

Now suppose, counter-factually, that the Wachau were and had always been completely cut-off from the world. What would the Wachau be like?

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Me, myself, and economics: Specialization versus Interdependency

According to Wikipedia, the probably most widely used and most broadly reviewed encyclopaedia on earth, and the references cited therein, economics as a term was suggested by economists in order to establish their science “as a separate discipline outside of political science and other social sciences”. Looking back at my study of economics, I have to say that we probably pursued this intention a bit too far.

The definition for economics as well as economic science to be found in textbooks, dictionaries, and encyclopaedias often reduces our subject to concerns about “production, distribution, and consumption of goods and services”. In addition, we commonly narrow our investigations further down to only those goods and services whose exchanges are market outcomes or are at least accompanied by official transactions.  At the end, we frequently draw conclusions about optimality with regard to welfare and utility while a huge part of interactions, which our utility and welfare depend on, is not even taken into account.

It simply may not be a good idea to separate economic science from other social sciences, while final conclusions about the economic system can hardly be drawn independent of the social system it is embedded in. Instead of narrowing our perspective, we should rather reconsider a broader definition of economic science which is still used in some textbooks, according to which we should deal with all of those human activities that serve the satisfaction of needs. This does not only extent our investigation to individual behaviour aside from markets. It also emphasizes that it may be fundamentally wrong to exclude normative considerations from economic analysis. If our welfare and utility also depends on the satisfaction of needs for things like fairness and equality, our concept of efficiency has to be refined.

This already suggests that also the intended separation from political science has to face limits. In addition, every exchange and negotiation, on markets or not, crucially depends on initial endowment and corresponding bargaining power. Endowment as well as power is not god-given. Just like markets are not god-given institutions. They are manmade and just like every law and order they root in temporary compromises. There is no property right that does not depend on normative rules in the past. There is no economic outcome that does not depend on the institutional framework determined by the political system in charge.

For the same reasons, there may be no separation of economics from other social and political sciences without a corresponding loss in validity of our conclusions. While we certainly have to specialize in our disciplines, our disciplines themselves should not specialize more than there interdependencies allow for.


Wikipedia, (last access 29.01.2017)
The Free Dictionary, (last access 29.01.2017)
Wöhe, Günter and Ulrich Döring (2008). Einführung in die Allgemeine Betriebswirtschaftslehre. 23rd ed. München: Vahlen. (p. 1)
Estrin, Saul, David Laidler, and Michael Dietrich (2008). Microeconomics. 5th ed. Edinburgh: Pearson Education and Prentice Hall. (p. 1)
Snyder, Christopher and Walter Nicholson (2008). Microeconomic Theory: Basic Principles and Extensions. 10th ed. Mason: South-Western. (p. 6)
Pindyck, Robert and Daniel Rubinfeld (2009). Mikroökonomie. 7th ed. München: Pearson Studium. (p. 27)

Rationales Entscheiden bei Radikaler Unsicherheit

Für diejenigen, die es verpasst haben oder es noch einmal sehen wollen! Hier ist ein Video meiner Antrittsvorlesung an der Universität Graz, vom 19. Oktober 2016:
Rationales Entscheiden bei Radikaler Unsicherheit“. Der Vortrag beruht auf meiner Arbeit “Abraham Wald’s Complete Class Theorem and Knightian Uncertainty“.

Resolving a family conflict with microeconomics

I was recently able to help family friends, a father and daughter, with a little family conflict using a bit of microeconomics. The problem was this. The daughter, let’s call her Marianne (not her real name) needed dental work. Her Austrian dentist was fully prepared to fix Marianne’s dental problem for a fee in the neighborhood of € 1000. Marianne’s father, let’s call him Franz (not his real name), tends to go to a dentist in a neighboring country and is very happy with his service there. He ascertained that his dentist would charge something in the neighborhood of € 100 for the same dental work. Marianne is a 20 year old student and still relies on her father to pay things such as dental bills for her. When I met them recently they were arguing over which dentist she should go to. In what follows I will explain their positions, and how a little bit of microeconomics helped with the resolution of this conflict, why it worked, and when it would not necessarily work.

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