mathematics of games
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.
( Enter your step-by-step answer and explanations here. )
2. Use the payoff matrix from number 1 to determine the optimum strategy for Club 1. Show all of your work.
( Enter your step-by-step answer and explanations here. )
3. Use the payoff matrix from number 1 to determine the optimum strategy for Club 2. Show all of your work.
( Enter your step-by-step answer and explanations here. )
4.
5. Find and interpret the value of the game.
( Enter your step-by-step answer and explanations here. )
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 |
( Enter your step-by-step answer and explanations here. )