My friend Scott who is a soccer fan and I watched the Spain v. Portugal semifinal of Euro 2012 yesterday afternoon. Of course whenever I watch a soccer game no goals are scores and after 120 minutes of play the game went to penalty kicks.
Penalty kicks can be modeled as a "simple" game theory scenario with goalie and shooter choosing strategies left, middle and right. Both players basically make the decision at the same time. If the goalie chooses the same strategy as the shooter it is likely a blocked shot, if the kicker and goalie choose different strategies usually a goal is scored. Making things more complex some kickers are better and kicking in particular directions and some goalies are better and moving certain directions. More complex is a kicker will chose to shoot based on what he believes the goalie will do. His beliefs will be based on the goalie's beliefs about the kicker's beliefs. This starts to get real complex real quick.
Chiappori, Levitt, and Groseclose looked at penalty kicks in the French and Italian soccer leagues. The best result is kicking it down the middle scores a goal 81% of the time compared to 76% for going left and 70% going right. So everyone now knows to kick it right down the middle, but now goalies know that so you still have to mix strategies.
The paper shows that a split second decision gets complicated pretty quick.
Tomorrow I leave for the Western Economics Associate meetings, where I'll attend lots of Sports Economics paper presentations. I'll blog about them when I get the chance.