Mathematics
Rasmussen College G&B Consulting Non-Zero Game Scenario Assignment

Rasmussen College

Question Description

Competency

This competency will allow you to demonstrate your ability and skill in analyzing nonzero-sum games and synthesizing optimal strategies within them.

Instructions

During the city's mayoral race, one of the candidates hires G & B Consulting. This candidate is one of two from the same party are vying to be put on the ticket. She believes that the nomination will likely come down to what stance she takes on a tax bill. The bill is for a tax increase that would subsidize education grants. Staying within traditional party lines would be advantageous to gaining support from the core constituency, but going against party lines on the issue would help sway swing voters and independents. To date, she has not had to make any declarative statements on the bill, but she also knows that it will inevitably come up at an upcoming debate.

If both candidates go along party lines, neither has a distinct advantage over the other. Likewise, if both candidates break from party lines, neither has the advantage. If the first candidate chooses to go along party lines while her opponent breaks, she would have the advantage in earning the nomination. If the first candidate chooses to break from party lines while her opponent does not, her opponent would have the advantage. This would result in the following payoff matrix:

Candidate 2

Stay

Break

Candidate 1

Stay

(0, 0)

(2, 1)

Break

(1, 2)

(0, 0)

Part 1: Determine the optimum strategy for each candidate showing all work and explaining your steps for inclusion in a final report to be delivered to the client. This strategy should be based purely on the analysis of the payoff matrix and not include any political stratagem or personal views so that you can provide the candidate with a purely objective approach.

Part 2: Create a summary report for the candidate that includes all relevant work done on the problem and a realistic interpretation of your solution.

Part 3: Shortly after delivering your final report, a local news agency releases some polling data that shows more accurate data about voters' preferences under the various possible outcomes. The new data results in the following payoff matrix:

Candidate 2

Stay

Break

Candidate 1

Stay

(0, 0)

(3, 1)

Break

(2, 3)

(0, 0)

As a professional courtesy, you take it upon yourself to follow up with your client after taking the new information into consideration. Compose an email to the candidate describing how this new data does or does not affect your prior solution. In an attachment to the email, include all relevant work with descriptions of your steps.

Final Answer

attached is my complete answer

Part 1:
The payoff matrix is shown below:
Candidate 2
Stay Break
Stay (0, 0) (2, 1)
Candidate 1
Break (1, 2) (0, 0)
Let m1 , m2 be moves and let a  m1 , m2  and b  m1 , m2  be candidate 1’s and candidate 2’s
payoffs if candidate 1 plays m1 and candidate 2 plays m2 . Then, for a given symmetric game, we
have a  m1 , m2   b  m2 , m1  and b  m1 , m2   a  m2 , m1  , which implies that for i, j 1, 2 ,
the entries in the j-th row and the is column is obtained from the entries in the i-th row and j-th
column by interchanging the payoffs. Now, using the above process, the payoff matrix becomes
Candidate 2
Stay Break
Stay 0+0=0 2+1=3
Candidate 1
Break 1+2=3 0+0=0
Let a  0, b  3, c  3, d  0 , which put the payoff matrix in the following form:
Candidate 2
Stay Break
Stay a
b
Candidate 1
Break c
d

The optimum strategy for candidate 1 is

d  c
a  b
| Stay,|
| Break 
d  c  a  b
d  c  a  b
 0  3 | Stay,|  0  3 | Break
|
 0  3   0  3
 0  3   0  3

|

3
3
| Stay,|
| Break
6
6
|1/ 2 | Stay,|1/ 2 | Break
|

The optimum strategy for candidate 2 is

a  c
b  d 
| Stay,|
| Break 
 a  c   b  d 
 a  c   b  d 
 0  3 | Stay,|  0  3 | Break
|
 0  3   0  3
 0  3   0  3

|

3
3
| Stay,|
| Break
6
6
|1/ 2 | Stay,|1/ 2 | Break
|

Final report:
Suppose that both ca...

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