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The Game Theory behind the World Cup Group Stage

The group stage of the world cup consists of eight groups of four teams, each vying for one of the top two spots in their group so they can advance to the single elimination portion of the tournament. Three points are awarded for a win, and one for a draw, so it seems obvious that the optimal strategy for each game is to try to win. This is not always the case however, as in some cases a draw can actually have as much utility as a win. An example of this is the 2014 World Cup where going into the last game of the group stage, the US and Germany led their group with four points, while Ghana and Portugal had one apiece. A draw between the US and Germany would see both teams advance, with Germany in first on goal differential. There is still a lot of incentive to win the game. A win would cause the team to finish first in the group, and avoid a talented Belgian side in the first round of the next stage.

The article discusses how this scenario is similar to the prisoner’s dilemma. Both teams would be happy if they drew and advance. The dominant strategy of both teams is to play to a win, because regardless of the stance their opposition takes, the team will be more likely to pick up points by not sitting back on defense. What then is preventing them from colluding and playing to a draw? As the article discusses, West Germany and Austria played to a 1-0 result in 1982 that allowed both teams to advance. While not punished by FIFA, the game is now referred to as the “Shame of Gijon”. There would be just as much of a social penalty today if the teams colluded and allowed each other to advance.

http://www.forbes.com/sites/whynot/2014/06/25/the-beautiful-game-theory/

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