Question

1. When a soccer player commits a foul in their own penalty area, the opposing player is awarded a free shot against the goalie called a penalty kick. If a player’s most accurate penalty kick placement is the upper-right corner of the goal, should she always try for the upper-right corner of the goal?

Answer 1

It will be pretty bad idea for the kicker to play a deterministic strategy i.e to kick to the upper right corner of the goal because now the goalkeeper will always jump to the upper right corner of the goal and stop the ball. This will yield negative payoff for the kicker as he is not able to score. So the player should not always kick to the upper right corner even though he is most accurate in that region.

So in such situations the kicker should adopt mixed strategy i.e he should sometime kick to the upper left corner or the bottom right corner. The idea behind the mixed strategy is to confuse the opponent by playing randomly.