You are the media manager for an incumbent candidate for the US Senate

You are the media manager for an incumbent candidate for the US Senate.  Your candidate has high negatives ever since he was caught writing checks on a campaign fund account for personal use.  There are 8 days left until the election and you are trying to decide the types of advertisements to air during the 6:00-7:00 pm local news show in the capital city of your state.  On any given day, you can afford to buy one 30 second spot per night during this show and your opponent will also probably air one 30 second ad per night as well.

The effect of your advertisement depends on the type of ad that your opponent runs.  Your candidate is particularly vulnerable to negative ads by your opponent.  You have conducted a series of focus groups that pit positive and negative ads for your candidate against positive and negative ads for your opponent.  The results of these focus groups are shown below.  The numbers in the table show projected gains and losses in percentage of previously uncommitted voters selecting your candidate in overnight polls after they watch the ads of the two candidates..

Your Opponent
You:        No Ad        Negative Ad Positive Ad
No Ad        0%        -1%        -3%
Negative Ad    +3%        +1%        -2%
Positive Ad    -1%        -3%        +2%

A. Solve this game using any appropriate technique.  Explain why you chose the technique and be sure to explain your answer and show your work.

HINT: Both the graphical technique and the algebraic technique for finding mixed solutions in 2×2 zero sum games work just fine with negative numbers.  Just follow the algorithms carefully and be sure to keep close track of the signs when using the formulas.  If you use linear programming to solve the game, you must add a constant to each cell to make all the numbers positive.  You must then subtract the constant from the value of the game that is found by solving the linear programming before you calculate probabilities.

B. What do you propose to your candidate?  That is, how does your result translate into actual actions in the campaign?  Given your result, what do you expect your opponent to do?

C. Your candidate is ahead in the poles by 2% now with 8 days to go until the election, do you think your candidate will win the race?  Why or why not?

Here’s the SOLUTION

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