Mathematics Of Games*****It has been used*****Use as a Guide Paper*****

  

Deliverable 04 – Worksheet

1. Market research has determined the following changes in market shares based on the different combinations of music choices for the two clubs: if both clubs play country, the new club (Club 1) does very well with a 24% increase in market share. If Club 1 plays country and the competing club (Club 2) plays rock, Club 2 gets a 12% increase in market share. If these choices are reversed, Club 2 does even better and gets an 18% increase in the market share. Lastly, if both clubs play rock, Club 1 does better and gets a 6% increase in market share. This results in the following payoff matrix:

  

Club 2

 

Club 1

Country

Rock

 

Country

(24, -24)

(-12, 12)

 

Rock

(-18, 18)

(6, -6)

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

  

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

3. Use the payoff matrix from number 1 to determine the optimum strategy for Club 2. Show all of your work.

4.  

5. Find and interpret the value of the game.

6. Working in parallel your co-worker wants to make the recommendation that the new club owner should always follow the schedule shown below. Do you agree or disagree with this strategy? Explain your reasoning.

  

Wednesday

Thursday

Friday

Saturday

Sunday

 

Country   

Rock

Country

Rock

Country