Learn your game theory

When you do, you won't be surprised by things that, after a moment's thought, aren't all that surprising.

Here's the situation: today in the last round of the World Cup Group A, Mexico played Uruguay while South Africa competed with France. These were last games of round one, and they were deciding which teams advance to the knock-off stage of the tournament (round of 16). Best two teams in the group advance, the other two are knocked out of the tournament. It pays to be the best team in the group, as it means that you will likely be paired up with a weaker team in the knock-off round (no. 1 team from group A plays with no. 2 team from group B and vice versa). The situation after previous two games was such that, in case of a tie between Uruguay and Mexico, both teams ensure that they qualify, regardless of the outcome of the South Africa-France game. Because of this, essentially all sports media have decreed that both teams will play for a scorless draw: they will both come out on the pitch with an unspoken understanding that, since a tie is good for both of them, and since not scoring is the safest and least suspicious-looking way of ensuring a tie, they will both avoid serious attempts at attacking the rival's goal.

The sports media couldn't be more wrong. If they they had any brains, they wouldn't be worried about this game being rigged. In fact, the only rational thing for both teams to do is to try to score and score early, because the situation that the teams are in is that of a classic Prisoner's Dilemma, and the only rational thing to do in a Prisoner's Dilemma is to not cooperate. Sure, it is good for either team to tie, but it's even better to win. If they win, they ensure a top spot in the group and thus raise their chances of avoiding Argentina in the next round; if they tie, they may be second (depending on what happens in the other game). Suppose you're Mexico's coach. It's the 88th minute of the game and the result is nil-nil because Uruguay has in fact "cooperated" by not trying to score on you. What do you do? Tell your team to score, of course; if you do, Uruguay will likely not have enough time to tie the game back, and so you will ensure yourself a win and the additional prize of avoiding Argentina. But the Uruguay coach knows that you face that incentive, so he will not cooperate in the first place. You know that the Uruguay coach will not cooperate, so you will not cooperate either. The only rational tactics ("equilibrium" in game theory lingo) is for both teams to try to score early to avoid being a "sucker" when it's too late in the game to retaliate. A tie is of course still a likely outcome of the game, but both teams will play for the win, not for the tie.

This is in fact what happened. Both teams were seriously trying to score. In the end, only one of them turned out to be successful (Uruguay won 1-0), but both tried to; neither team was faking their attacks. (Mexico still qualified because they lucked out in terms of the score in the other game.) Sports media call this result "surprising" and salute Uruguay for being "spontaneous" and "non-calculating." The truth is exactly the other way around. The result is not surprising, and Uruguay's tactics were calculated and rational.