With the 2010 (football/soccer) World Cup well underway, it’s only a matter of time before some teams will have to face the heartbreak of leaving the competition due to a missed penalty.
In the “knockout” stages of a football competition each match must produce a winner. If the teams have scored equal number of goals (after additional playing time), the game will be decided on “penalties”. A penalty is a free kick taken from directly in front of the goal, with only the defending goalkeeper between the penalty-taker and the goal.
A professional football player will put the ball in the back of the net in about a quarter of a second. This doesn’t give the goalkeeper enough time to respond, so he must anticipate the likely trajectory of the ball—for example, by diving to the side that the penalty-taker tends to prefer.
Of course, the penalty-taker wants to mislead the goalkeeper. While the penalty-taker may be stronger shooting, say, to the right, doing this every time would make his actions too predictable.
So, the goalkeeper and penalty-taker must optimize their own strategies without knowing the strategy that will be adopted by the other party. This is the type of decision-making activity that can be effectively studied using game theory. The players are attempting to optimize their “payoffs”.
Using game theory we can see that the optimal strategy for both players is to behave unpredictably. They must balance their strengths (e.g. the penalty-takers’ strong side) with the value of potentially misleading the other player. But how does this help your team lift the FIFA World Cup Trophy?
Well…it turns out that most professional football players are also expert economists. A few years ago Ignacio Palacios-Huerta demonstated that top players act in accordance with the theory—i.e. they optimize their penalty-taking strategies. While this may come as a shock to some fans, one can’t argue with the science…
Maybe, once the World Cup is over, we can convince some of the players to pop into their respective finance ministries and offer a bit of advice…