# Deliverable 05 Worksheet

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Mathematics
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Deliverable 05 Worksheet
1. Market research has determined the following changes in the polls based on the
different combinations of choices for the two candidates on the tax bill in the upcoming
debate:
Use this payoff matrix to determine if there are dominant strategies for either player.
Find any Nash equilibrium points. Show all of your work.
Incumbent
Challenger
Stay
Break
Stay
(0, 4)
(3, 0)
Break
(1, 2)
(2, 3)

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Incumbent
Challenger
Stay
Break
Stay
(0, 4)
(3, 0)
Break
(1, 2)
(2, 3)

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Deliverable 05 – Worksheet 1. Market research has determined the following changes in the polls based on the different combinations of choices for the two candidates on the tax bill in the upcoming Challenger Incumbent Stay Break Stay (0, 4) (3, 0) Break (1, 2) (2, 3) debate: Use this payoff matrix to determine if there are dominant strategies for either player. Find any Nash equilibrium points. Show all of your work. Challenger Incumbent Stay Break Stay (0, 4) (3, 0) Break (1, 2) (2, 3) Fix Incumbent to choose stay. Challenger chooses break. Fix Incumbent to choose Break. Challenger chooses Break So, Challenger Dominant strategy is Break. Fix Challenger to choose Stay. Incumbent chooses stay. Fix Challenger to choose Break. Incumbent chooses stay. So, Incumbent Dominant strategy is stay. break,Stay are the Nash equilibrium points as well. 2. Use the payoff matrix from number 1 to determine the optimum strategy for your client (the challenger). Show all of your work. Challenger Incumbent Stay C q Break D 1-q Stay A p (0, 4) (3, 0) Break B 1-p (1, 2) (2, 3) Challenger creates indifference in Incumbent by balancing the expected values of Incumbent’s choice i.e. E stay c = E break d 4p+2(1-p) = 2p+2 0p+3(1-p)= −3p+3 2p+2 = −3p+3 P = 1/5 Challenger chooses stay A 1/5 of the time and chooses b 4/5 of the time randomizing the order of choices. 3. Use the payoff matrix from number 1 to determine the optimum strategy for the incumbent. Show ...
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