# Rasmussen College Optimal Strategy with Zero Sum Game Worksheet

Description

Assignment Content

Competency

This competency will allow you to demonstrate your ability and skill in analyzing zero-sum games and synthesizing optimal strategies within them.
Instructions

A night club owner has just changed ownership and the new owner has contracted G&B consulting to help decide the direction the club will take. Based on the local music scene, it would make the most sense to book either rock bands or country bands. The new owner is aware that a competing night club is hoping to attract new customers while the new club is getting itself established. Since these are the only two night clubs in town competing to book the same bands, whatever market share is gained by one is lost by the other making this a zero-sum game. The new club owner has hired you to find the optimum strategy for this situation.

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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 12% increase in market share. If Club 1
plays country and the competing club (Club 2) plays rock, Club 2 gets a 6% increase in
market share. If these choices are reversed, Club 2 does even better and gets an 9%
increase in the market share. Lastly, if both clubs play rock, Club 1 does better and gets
a 3% increase in market share. This results in the following payoff matrix:
Club 1
Club 2
Country
Rock
Country
(12, -12)
(-6, 6)
Rock
(-9, 9)
(3, -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.
2. Use the payoff matrix from number 1 to determine the optimum strategy for Club 1.
3. Use the payoff matrix from number 1 to determine the optimum strategy for Club 2.
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
Rock
Country
Rock
Country
Rock

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6 Questions

Tags:
market research

Payoff Matrix

Zero Sum Game

Nash equilibrium points

Market Shares

Optimal Strategies

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