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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?

          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?

Show more…

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?

Added by Christina O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

06/03/2022

Step 1

Step 1: To find the Nash Equilibria, we need to look for situations where neither player has an incentive to change their strategy, given the other player's strategy. Show more…

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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 50% 50% 90% 10% FAU pass 60% 40% 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 30% 70% 90% 10% FAU pass 60% 40% 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?

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Transcript

00:01 Anyway, everyone, so this is the question that we have.

00:02 We have a football game.

00:05 We have a football game played between two teams.

00:10 So we have this data of two point conversion, which is of defense, defense, defend against, against wide run, and defend against middle.

00:45 We have run wide left run up middle and run up right this is defense so this is offense this is 7 .7 and 0 .3 this is 0 .4 and 0 .6 this is 0 .7 this is 0 .4 and 0 .6 this is 0 .7 .3 this is 0 .4 0 .6, this is 0 .5, 0 .5, this is 0 .4, comma, point six.

01:37 Now, we have five questions associated.

01:42 Part a, we have to find that defense expected from playing the pure strategy, defend against wide run.

01:58 Part b, that is, offense.

02:01 Offense offenses by playing pure strategy of run wide left part c we have in an m e what is the probability probability that defense defense against wide run depends against wide run part d what is the probability what is the probability probability that offense runs up the middle runs up the middle and part e is probability probability that offense runs wide left so let's jump on to the solution of the question so let us first of all denote so let p be the probability probability probability that offense choose, offense choose, run wide, that q be the probability, probability that wide, right.

03:50 And 1 minus p minus q would be the probability that runs up middle because nothing is left.

03:59 Runs up middle.

04:02 So if i have these strategies, so this is going to be, so this is going to be runs up middle.

04:14 So this implies let's put in the values...

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