How Not to Think Strategically, pt 1351
"...The stance from football's governing body is that the officials have got it about right so far in Germany, despite the apparent card frenzy.
Fifa spokesman Markus Siegler rejected the notion that the extraordinarily high number of cautions was a paradox.
"You could say if the referees were not active, it could have turned out into a more unfair or dirty tournament," he said."
See, the thing about incentives is that they're often paradoxical.
In this case, Fifa doesn't understand that the incentive to foul is, in large part, set by the refs, not the players (or, more accurately, they're pretending not to understand it).
Let's say I am a player. If a ref is being liberal with cards, am I better off fouling, or not fouling? I am always better off not fouling - but only if everyone else does too. If everyone else fouls, I am always better off fouling, since it's likely my team will be penalized anyways.
In other words, this is a classic multiplayer Prisoner's Dilemma - after a certain point, the harsher refs are, the more fouls we should expect (as, I guess, any fan could have told you without the game theory).
Lets say I'm a player who knows economics. If a ref is being liberal with cards am I better off fouling, or not fouling?
I am better off fouling if the cost of the foul (i.e. the card) is less than the payoff. If every one else fouls, then they are being silly and have an increased chance of getting sent off or missing the next game. My choice is independent of the other players' choices.
In other words, this is a classic cost vs benefit decision. The harsher refs are, the less fouls we should expect (as any fan could have told you assuming a modicum of common sense)
// Brian Azzopardi // 4:17 PM
There's an existence proof that your logic is off - the World Cup :)
It's the same analysis that Fifa has used to disastrous effect.
The flaw in this logic is that players' choices are of course not independent - rather, they are interdependent.
Think about it this way - if a ref is liberal with cards, I am better off diving and fouling - because so is everyone else.
Thx for the comment.