optimal-strategy-with-zero-sum-game

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 local night club 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 and will be considering their own strategy. Since these are the only two night clubs in town competing to book the same bands, whatever market share gained by one is lost by the other, making this a zero-sum game.

After doing some market research, you have found that the night club owner should expect the following results: if both clubs play country, Club 1 does very well with 20% more market share than Club 2. If Club 1 plays country and Club 2 plays rock, Club 2 comes out ahead instead, getting 10% more market share than Club 1. If these choices are reversed, Club 2 does even better and gets 15% more market share. Finally, if both clubs play rock, Club 1 comes out slightly ahead with 5% more market share than club 2. This results in the following payoff matrix:

		Club 2
		Country	Rock
Club 1	Country	20	-10
	Rock	-15	5

Part 1: Use the payoff matrix to determine the optimum strategy for the owner of Club 1. Show all relevant work, and describe your steps so that you can give a complete explanation in your final report to the club owner.

Part 2: Working in parallel, a coworker has found the same optimum strategy as you and has come up with the following schedule for Club 1:

Wednesday	Thursday	Friday	Saturday	Sunday
Rock	Rock	Country	Rock	Country

Before the two of you compile your work into a final report, you need to decide if you are in agreement in all aspects. Compose an email to your coworker with your conclusion. Be sure to include any flaws you find in your coworker’s solution with evidence in the form of work shown.

Part 3: Create a report that details how you would advise the club owner including all relevant work used in devising your strategy.