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.
- 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.”
- 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.
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?
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“.
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.
There is a period of time each summer when many members of my wife’s fairly large family all come together in one large house. People take turns (to some degree) cooking dinner. In this post I describe what happens when dinner is ready and try to explain it using a bit of game theory.
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.
This is about driving on Cornish lanes (small roads in Cornwall, UK). I offer two things in this post: informed casual observations (in place of rigorous data collection) about how people navigate these lanes and a bit of game theory to explain my casual observations.