If a soccer game ends in a tie it goes into a penaltykick sh

If a soccer game ends in a tie, it goes into a penalty-kick shootout in which each team chooses five players to take penalty kicks. The team that makes the most subsequent penalty kicks wins the game . In a penalty-kick shootout, the shooter and the keeper each decide simultaneously on a direction to move. They can choose left, right or middle. These strategies yield the following game theory table, where the first value is the shooter\'s probability of scoring and the second value is the keeper\'s probability of stopping the shot:

0.90,0.10

0.85, 0.15

This is an example of a constant-sum game since each pair of entries in the game theory table sums to 1. This can be analyzed in the same manner as a zero-sum game.
a. Use the dominance to reduce the game to a 2x2 game. Which strategies are dominated?
b. What is the solution to this game for the shooter and for the keeper?
c. What is the shooter\'s expected probability of scoring?

Solution

0.90,0.10

0.85, 0.15

By applying dominanance rule :

Strategy =

Shooter = Right

Keeper will select right strategy with probabilty = 0.55

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Solution for game

Shooter :Shouter will select right strategy

Keeper : Keeper will select right strategy

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shooter\'s expected probability of scoring

= 0.85