Question 5: Applications of Game Theory: Mixed Strategies
FAU and FIU have good scout teams that can estimate the likelihood of successfully executing a play in any
situation. The following game table represents the payoffs for each team, which equals the probability that each
team will successfully execute a play given the strategies played. No prior knowledge of football is necessary to
answer this question, and no football terminology is expected in your answer other than the strategies provided.
FIU
run defense pass defense
run
FAU
pass
50% 50%
60% 40%
90% 10%
20% 80%
5a) Solve for all Nash Equilibria in pure strategies and mixed strategies (if none, indicate zero).
Now assume that FIU's defense against the run strategy improves, and results in a change in the probability of a
successful play execution as follows:
FIU
run defense pass defense I
run
FAU
pass
30% 70%
60% 40%
90% 10%
20% 80%
5b) Given FIU's improved ability to defend against the run, how does this change FIU's optimal play mix (q^)
and the resulting Nash equilibrium?
5c) Will FIU use its run defense more now that it has become better at it? Why or why not?
