Optimal Strategy With A Nonzero-Sum Game

During the city's mayoral race one of the candidates hires G&B Consulting. This candidate is a challenger from the same party as the incumbent mayor and is vying to be put on the ticket in the general election. She believes that the nomination will likely come down to what stance she takes on a proposed 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. The issue is bound to come up at an upcoming debate and she wants the help of G&B Consulting to determine an optimum strategy.

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.

 

 

 

1. Use the payoff matrix from number 1 to determine the optimum strategy for your client (the challenger).  Show all of your work.

 

 

 

 

1. Use the payoff matrix from number 1 to determine the optimum strategy for the incumbent.  Show all of your work.

 

 

 

1. 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.

 

 

 

 

 

1. 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.