Reference no: EM132308707
Part 1 - Variable Sum Games
Q1. Find the Natural Outcome of the following variable sum game and answer the questions below.
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I
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II
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A
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2, 3
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4, 2
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B
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1, 1
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3, 4
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a. Explain how you found the Nasal Outcome.
b. Is the Natural Outcome an equilibrium?
c. Is the Natural Outcome Pareto optimal?
d. Is the Natural Outcome vulnerable to a threat by the row player?
e. Is the Natural Outcome vulnerable to a forced move by the row prayer?
Q2. Using cell A(I) in game 1 above as the initial state, solve game 1 using the theory of moves.
a- Do you get a afferent result from the natural outcome? Why or why not?
b. Is the outcome of the Theory of Moves an equilibrium?
c. Is the outcome of the Theory of Moves Pareto optimal?
Part 2: Zero Sum Games
Q3. Solve the following game using whatever method is appropriate. Show your work and explain how you found your answer.
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I
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II
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III
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A
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18
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32
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17
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B
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21
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36
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31
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C
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10
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5
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40
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Q4. Solve the following game using whatever method is appropriate. Show your work and explain how you found your answer.
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I
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II
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III
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IV
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A
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43
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39
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23
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18
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B
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48
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43
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33
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23
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C
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23
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9
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23
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18
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D
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18
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13
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37
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42
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Part 3 - Word Problems
Q5. The United States is considering withdrawing from the Iran Nuclear dear. European leaders are urging the US to remain in the deal. It is unclear if the Europeans will follow suit if the United States withdraws from the deal and imposes economic sanctions on Iran again. The can be shown in a simple variable sum game.
- The players are US and the Europeans.
- The US has two choices, impose sanctions or not impose sanctions.
- The Europeans have two options, impose sanctions or not impose sanctions.
The payoff table looks like this
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Game A
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US
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Europeans
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US
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Europeans
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Sanctions
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Sanctions
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4
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2
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US wants full participation in sanctions, Europe doesn't want any sanctions
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No Sanctions
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3
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3
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US wants sanctions with or without Europe, Europe doesn't want sanctions
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No Sanctions
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Sanctions
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2
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1
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It doesn't make sense for the Europeans to create Sanction if the US doesn't
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No Sanctions
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1
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4
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Europeans would be happy with no sanctions but the US would find this unacceptable
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The US has threatened to punish the Europeans with trade restrictions if they do not follow suit and impose sanctions on Iran. This can be modeled in a different game with the following payoff table.
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Game B
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Europe
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USA
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Europeans
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US
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Sanctions
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Punishment
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1
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1
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It doesn't make sense for the US to punish Europe if they agree to the sanctions
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No Punishment
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3
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4
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US wants sanctions without having to punish its allies
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No Sanctions
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Punishment
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2
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2
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Europe wants no sanctions and the US wants to avoid punishing its allies.
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No Punishment
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4
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3
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Europe wants no sanctions and no punishment, US wants sanctions but really doesn't want to punish its allies
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Create a game for each of these payroll tables and answer the following questions for each game
1. What is the Natural outcome?
2. Is the Natural Outcome Pareto optimal?
3. Is the Natural Outcome an equilibrium?
4. Is the Natural Outcome threat vulnerable?
5. Is the Natural Outcome force vulnerable?
Wnte a short essay that describes what each of these games ridcate about what might happen (1 - 2 paragraphs).
Q6. 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 at du-wig 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 might during this show and your opponent will also probably air one 30 second ad per right 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..
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Your Opponent
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No Ad
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Negative Ad
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Positive Ad
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You:
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No Ad
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0%
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-1%
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-3%
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Negative Ad
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+3%
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+1%
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-2%
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Positive Ad
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-1%
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-3%
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+2%
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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 2x2 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 polls by 2% now with 8 days to go until the election, do you think your candidate will win the race? Why or why not?