The strategies in a soccer game can be considered from the perspective of game theory as a two-person, zero-sum game: This is correct since in each play, the game is zero-sum since the yards won by one team are exactly what the other loses. In addition, each team selects its strategy before knowing that of its opponent.

Considering Team A as the offensive team trying to gain yardage and Team B as the defensive team trying to keep A's yardage to a minimum, we can define Team A's strategies as:

• a1 = rushing play
• a2 = air pass play and
• a3 = blitz (not sure if this is an offensive play but assume it that way for game purposes).

Those of team B would be:
• b1 = ground carry defense
• b2 = air pass defense and
• b3 = blitz defense

It is observed then that for a soccer game a mixed strategy game is more convenient since it would not be effective to always play the same strategy. Therefore, Team A will be varying the selection of their offensive strategies while Team B, meanwhile, will be making a mix or variations of their defensive strategies.

Suppose you have the following table of yards gained by team A depending on the strategy selected by the two teams:

Team B
Team A	Strategy	b1	b2	b3
	a1	0	-1	2
	a2	5	4	-3
	a3	2	3	-4

a) Explain why in this case the minimax criterion of a pure strategy cannot be applied?
b) Identify dominant strategies, if they exist.
c) Determine the strategies of each team and the value of the game