http://www.econ.brown.edu/fac/ipalacios/pdf/professionals.pdf

The aim of this course has been to build mathematical models for various behaviors and phenomena within networks.  I tend to ask myself while doing homework: how well do people actually follow these models?  This paper by Ignacio Palacios-Huerta provides one case in which they do.

In the game of soccer, a penalty kick can be seen as a two player game.  The striker must choose a direction in which to shoot and the goalkeeper, standing 12 yards away, must guess which direction the striker will aim for.  Most games have many compounding variables making real world application difficult, but the case of penalties is fairly straightforward - strikers can either chose left, right, or center based on his own technique and what he predicts from the keeper.  A striker might favor one side due to his technique, but if that increased ability improved his chances at all, the keeper responds since he knows that the striker favors that side, thus lowering the chances of success to that favored side.

Palacios-Huerta’s study, in short, found that the mathematically derived mixed-strategy Nash equilibrium predictions for keeper and striker are nearly identical to the actual aggregate values observed.

The study provides a reassuring real world application of game theory.  It takes me a few minutes to calculate a mixed-strategy Nash equilibrium sometimes, but its easy to forget that this is being used to calculate what happens without any calculation in a real world scenario.