Mia Has Been Awarded a Penalty Kick

Essay

Mia has been awarded a penalty kick.China's goalie has two possible strategies,to dive left or dive right.Mia can shoot left or shoot right.There is no time for the goalie to determine where the ball is going before she must commit herself to diving left or right.Suppose that the goalie always stops the shot if Mia shoots right and the goalie dives left.On the other hand,Mia always scores if she shoots right uncontested.Mia is not as adept at shooting to the left.When Mia kicks left the goalie stops the shot 75 percent of the time if she dives right,and Mia misses the open goal half the time when shooting left.
a)Summarize this game in a payoff matrix.
b)Does either player have a dominant strategy? Explain.
c)What is the Nash equilibrium? Explain.