Most professional sports have aspects that are zero-sum (there is a winner and a loser) and a simultaneous decision process. One such case is a shootout in soccer or hockey. Assume that the following table defines the probability of scoring for the offense, followed by the probability of the offense not scoring (which is the defensive payoff). Shooter \ Goalie Guess Left Guess Right Shoot Left 70, 30 90, 10 Shoot Right 80, 20 50, 50 a) For the Nash equilibrium of this game, what is the strategy for each of the shooter and the goalie, and what is the probability that the shooter scores?

b) Explain the concept of the Nash equilibrium in general terms - why must the shooter and the goalie choose that particular strategy in a Nash equilibrium