By John Considine
One of the sports economics books that I most enjoyed reading is Beautiful Game Theory. The title is a clever combination of Game Theory and the Beautiful Game. The subtitle is "How Soccer Can Help Economics". One way soccer can help economics is by using data from the beautiful game to test economic game theory. Penalty kicks feature prominently in Beautiful Game Theory as a way of examining if humans can make decisions in practice as suggested in theory. But one needs to be careful because the data is being shoehorned to match the theory.
The economic game theory used presumes that the interaction between penalty kicker and goalkeeper is a simultaneous game. It is not. It is close but the decisions are not made simultaneous. To illustrate examine the penalties in this video brought to my attention by Robbie Butler. Below is an image from the video. The goalkeeper has obviously begun the process of diving to his right (to the left as we look) before the ball is kicked. The ball is being kicked after the keeper has started his dive. The dive and the kick are not simultaneous. The decision about which side to kick the ball does not have the uncertainty presumed in deriving the minimax solution.
The economic game theory used presumes that the interaction between penalty kicker and goalkeeper is a simultaneous game. It is not. It is close but the decisions are not made simultaneous. To illustrate examine the penalties in this video brought to my attention by Robbie Butler. Below is an image from the video. The goalkeeper has obviously begun the process of diving to his right (to the left as we look) before the ball is kicked. The ball is being kicked after the keeper has started his dive. The dive and the kick are not simultaneous. The decision about which side to kick the ball does not have the uncertainty presumed in deriving the minimax solution.
Relying on penalty kicks to test if players play minimax is less than ideal. Ignacio Palacios-Huerta, the author of Beautiful Game Theory, understands this issue. The first chapter is titles "Pele Meets John von Neumann in the Penalty Area". Here the economist takes data from previously played games of soccer. The second chapter overcomes the problems identified above by taking soccer players to a laboratory to see if they play minimax in a different setting. Here the players play a game designed by the econo mist. The chapter is called "Vernon Smith meet Messi in the Laboratory". The sequencing of players and economists names in both chapters is not an accident.
Palacios-Huerta understands the difference between simultaneous and sequencial games. He famously advised the Chelsea goalkeeper not to dive early when facing Ronaldo in the 2008 Champions League Final. Ronaldo did not score.
Palacios-Huerta understands the difference between simultaneous and sequencial games. He famously advised the Chelsea goalkeeper not to dive early when facing Ronaldo in the 2008 Champions League Final. Ronaldo did not score.
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