# Optimal Strategy with a Nonzero-Sum Game

###### Presentation on Game Theory Applications
November 30, 2019
###### Choosing How to Entertain Yourself Is Simple
November 30, 2019

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:

Incumbent

Challenger

Stay

Break

Stay

(0, 4)

(3, 0)

Break

(1, 2)

(2, 3)

Use this payoff matrix to determine if there are dominant strategies for either player. Find any Nash equilibrium points. Show all of your work.

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 4>0. Challenger dominant strategy is to break 0<3 2. Use the payoff matrix from number 1 to determine the optimum strategy for your client (the challenger). Show all of your work. 1/5=20% Challenger will break 20% of the time and stay the other 80% of the time. 3. Use the payoff matrix from number 1 to determine the optimum strategy for the incumbent. Show all of your work. 4. Knowing that flip-flopping on an issue is worse than taking a stand on either side, you must recommend a single strategy to the client to take in the upcoming debate. Take into account the predictability of the incumbent’s strategy and assume rationality by both players. 5. Working in parallel your co-worker finds that there is a 60% chance that the incumbent will choose to stay within party lines. Does this agree with your findings? If not, identify the error made by your co-worker.