Penalty kick left right Nash equilibrium by Ciro Santilli 34 Updated +Created
When taking a penalty kick in soccer, the kicker must chose left or right.
And before he kicks, the goalkeeper must also decide left or right, because there is no time to see where the ball is going.
Because the kicker is right footed however, he kicker kicks better to one side than the other. So we have four probabilities:
  • goal kick left keeper jumps left
  • goal kick right keeper jumps right
  • goal kick left keeper jumps right. Note that it is possible that this won't be a goal, even though the keeper is nowhere near the ball, as the ball might just miss the goal by a bit.
  • kick right and keeper jumps left. Analogous to above