Game Theory 101: Soccer Penalty Kicks

In honor of the 2010 World Cup, William Spaniel shows how to optimizing kicking and defending penalty kicks. Should the kicker kick to his stronger side more often? The answer may surprise you.

Note: This is a complete information game. If the goalie doesn't actually know which side is the kicker's weak one, then the equilibrium will be different.

Category:

Education

Tags:

• game
• theory
• explained
• pure
• mixed
• strategy
• nash
• equilibrium
• solved
• soccer
• World
• Cup
• 2010
• penalty
• kick

[niallsp]

how come it was UL = theta KL and UR = theta KR but when you set them equal they both became KL?

[JimBobJenkins]

@niallsp The utilities are for the goalie and the sigmas (not thetas) are for the kicker. Both sigmas are for kicking left, so that should resolve the issue.

[niallsp]

@JimBobJenkins oh, so in the video it should have been UL = Sigma KL and UR = Sigma KL?

[JimBobJenkins]

@niallsp I think it is like that in the video...no?

[CogitoErgoCogitoSum]

Hold on. You arbitrarily stick a -1 in there... and understandably so. But you could just as easily have stuck in a -2, -3, so forth. Or different values for each. The point of putting a negative point of any value in there is to force the goalie to make a reasonable decision. But if their values are arbitrary then your MSNE has an arbitrary distribution.

[JimBobJenkins]

@CogitoErgoCogitoSum The MSNE is not an arbitrary distribution as long as both of the negative numbers are the same, and it wouldn't be sensible to model it with different numbers. (That would be like I am more okay with giving up a goal to the right than I am to the left, which is...strange.)

[9H0A0L0]

so kick center dumbass!

seriously why should the utility become 0.5?? with symmetric utility you don't have to be a genius to obtain 1/2 and 1/2 without game theory

[USSgordon]

@CogitoErgoCogitoSum The -1 is for how much the soccer players Team lost for the opposition scoring the point. since it was one point the goalie loses one point.

[billaudesvarennes]

So because the kicker knows that the goalie knows his stronger side and will defend that side more frequently, it does not make sense to play his stronger side more frequently, thus the kicker will assign a higher probability to his weaker side (knowing that the goalie will cover that side less frequently). So this is actually realistic (given that both have complete information). I think now I got it, thanks a lot!!!

[JimBobJenkins]

@billaudesvarennes This is saying that if both players know the kicker's stronger side, this is not a sensible strategy.