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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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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Reinhard Selten (October 5, 1930 – August 23, 2016)

Heute habe ich per Post die neueste Ausgabe des German Economic Review, ein „Special Issue in Honor of Reinhard Selten’s 85th birthday“ bekommen und gleichzeitig zu meiner Trauer erfahren, dass Reinhard Selten, einer der Begründer der modernen Spieltheorie und Wirtschaftsnobelpreistäger 1994 (gemeinsam mit John Nash und John Harsanyi), gerade vor einigen Tagen  verstorben ist. Die Wirtschaftswissenschaften haben damit einen ihrer bedeutendsten Vertreter verloren.

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Would a second Referendum on Brexit change the result?

A number of the Brexit (Leave) supporters are now unhappy with the actual outcome of the 23 June Referendum.

Is it because they were made aware of some new information? Apparently not all the promises that were made by the Leave campaign will be honored.

It is, however, possible that a second Referendum could change the result even if there were no new information about the consequences of a possible British EU exit. This possibility is to do with strategic thinking.

The typical voting model of a zero one decision (stay or leave the EU, in the present case) is such that all voters simply have a preference over the two outcomes. Some prefer to stay, some prefer to leave. If this is the case, voters do not have to engage in deep strategic thinking to simply vote their preference. In game theory jargon “voting for one’s preferred outcome is a (weakly) dominant strategy”.  The referendum will then simply demonstrate which of the two outcomes is favored by more people. Another referendum without any new information cannot change the result.

In the present case, however, many voters started googling “What is the EU?” only after the result of the Referendum became clear. Could it be that at least some of the leave voters did not really want to leave but simply wanted to make a statement of dissatisfaction? If this is the case, then some voters’ preferences could be as follows. Yes, they would prefer to stay in the EU, but they would like the result to be close. If you have such preferences and think that the result will be clearly in favor of staying in the EU – the bookies always saw Stay as the much more likely outcome – then you might cast your vote for the Leave campaign.

If enough people think so, then the ultimate outcome could be paradoxical. A majority of people vote to leave even though a majority of people actually prefer to stay. If this is the case a second referendum might correct this and reveal the true sentiment of British voters on the EU.