On Thursday, USA will play Germany in a game. The goal of this game is not to score more goals than your opponent. No, there is no soccer ball in this game. There are no corner kicks or yellow cards. This is not a soccer game.
This is a game of strategic decision making. And strategically, USA and Germany shouldn’t even bother playing that other game – the soccer game. When the opening whistle blows, the two teams should stand there and do nothing for 45 minutes. They should leave the ball at midfield and talk to each other about food and family and the weather. They should then take a break, come back out, and repeat the earlier 45 minutes.
The upcoming USA-Germany game is a perfect example demonstrating the principles of game theory.
Game theory is a branch of economics that focuses on the strategic interaction between two (or more) parties. Roger Myerson, a highly-regarded economist whose work mostly involves game theory, defines it as "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
Game theory was first academically discussed in the late 1920s by Hungarian mathematician John Von Neumann. Von Neumann’s work with game theory was motivated by his interest in poker. The scholar believed that poker was not solely a game of probabilities; poker also involved “bluffing” and strategy. Von Neumann went on to publish an article in 1928 titled “Theory of Parlor Games” and then a book titled Theory of Games and Economic Behavior.
Traditionally used in fields such as business, politics, and psychology, game theory can also be applied to another field – one with 22 players on it.
For the sake of argument, assume the primary goal of both USA and Germany (and any team, for that matter) is to advance out of group play and into the knockout round. (Yes, there are advantages to being seeded first, but they aren’t worth the risk of not advancing it all.)
If USA draws, it advances. If Germany draws, it advances. If one team wins and the other loses, then the losing team’s fate rests on tiebreaker scenarios and may not advance at all.
This situation is like a wrapped-up Christmas gift from the gods of economics looking for a real-life application of game theory. The coach of the USA team? Jurgen Klinsmann, a former German player who coached Germany in the 2006 World Cup. The coach of the German team? Joachim Löw, a former assistant of Klinsmann on his 2006 team.The rational decision would be for the two teams to cooperate and intentionally play for a draw. This would ensure each team advances. Playing for a win opens the possibility of ending with a loss (and subsequently, not advancing).
Frankly, however, the two teams aren’t going to just stand there for 90 minutes. They might play less aggressively, but they likely won’t cooperate for the sake of a draw. What would happen though, if they acted rationally and cooperated? They would shed light on another principle of game theory – the grim trigger strategy.
This strategy begins with two parties cooperating. When the whistle blows, imagine that Germany kicks the ball backwards and passes it amongst its defense. The two teams are still cooperating; they’re playing for a draw. Germany has the ball, but it isn’t trying to score. USA players are running around, but they aren’t trying to steal the ball.
Then, Germany advances the ball and tries to score. It is no longer cooperating for a draw. This deviation is defined as a trigger; it triggers the USA to stop cooperating as well, for the rest of the game. “Well if Germany is going to try and score, then we are too.” USA no longer trusts Germany to cooperate. As soon as one team stops cooperating, the other team loses its incentive to cooperate.
In the 1982 World Cup, West Germany infamously defeated Austria 1-0. After Algeria and Chile played a day earlier, West Germany and Austria were fully aware of the result needed to advance. If West Germany defeated Austria by one or two goals, both teams would advance. After grabbing an early lead, both teams were content with the outcome and rarely created additional scoring chances. In response, FIFA mandated that, in the future, final games within a round must be played simultaneously. This would have prevented West Germany and Austria from cooperating. While this effort lessened the possibility of two teams cooperating, it did not fully eliminate it.
In the 2010 World Cup, Mexico and Uruguay both led Group A with four points. South Africa and France trailed, each with one point. With Mexico and Uruguay playing each other in the last round of the group, the two countries would both advance with a draw. If one team lost, its fate would rest on the South Africa-France game and a possible tiebreaker.
In the 1st minute, Rafael Marquez of Mexico took a shot from 40 yards out. Mexico tried to score, and any notion of a “friendly draw” disappeared. In the 12th minute, Luis Suarez put his first shot on net. In the 43rd minute, Suarez scored the only goal of the match, giving Uruguay a 1-0 victory. (South Africa defeated France, giving both South Africa and Mexico four points. Mexico advanced on the tiebreaker.)
Thursday’s game could start with an agreement to play for a draw. (In theory, it should. In reality, it won’t.) The grim trigger strategy highlights the following principle: even if USA and Germany were to agree to play for a “friendly draw”, the two would stop cooperating once one team attempted to score. Unless USA and Germany play a soccer game with no scoring attempts, a “friendly draw” is implausible. As soon as one team makes a legitimate effort at scoring, the idea of cooperation falls apart.
There’s been much said about the Group of Death. On Thursday, we’ll find out just how grim it is.