See attached file, please.

Competency

This competency will allow you to demonstrate your ability and skill in applying game theory to real world scenarios.

Instructions

After working for 18 months in your analyst position at G&B Consulting, you are now being considered for a project manager position that would put you in charge of several team members. As part of the interview process, you have been asked to make a presentation to highlight what you think are the most compelling reasons you should get the position.

The first item you want to highlight is your customer satisfaction record. Over the past 18 months of employment you have worked with 24 clients, and according to the customer satisfaction surveys all clients are asked to take after their contract is completed, 22 of them rated you with the highest level of satisfaction. Use this information to find the best predicted probability of having a new client give the highest level of satisfaction.

However, having a single satisfied customer is not enough. It is very important to G & B Consulting that they maintain high ethical standards and continue to receive the highest rating from the Better Business Bureau consistently. In order to maintain this rating, the company must maintain a consistent customer satisfaction rating of 85% or higher. Internal projections predict that G&B Consulting will serve 60 clients over the next year. If you become the project manager and use your prior record as an indicator, find the probability that 85% or more of new clients will give the highest level of customer satisfaction rating. Show all calculations and formulas used. If you use Excel for your calculations include that along with your submission. Use this information to make a convincing argument that you are a good choice for the position.

The other item you wish to highlight comes from some work done for a local manufacturer. They believed that a competitor was illegally using one of their patents in their own manufacturing process and were considering litigation. This competitor's product were directly cutting into the manufacturer's profit, so they wanted to prevent the competitor's product from being made and recoup those lost profits. Of course, the litigation process is long and costly, and the outcome is not guaranteed and would likely result in a countersuit brought by the competitor. Before continuing with costly legal counsel, the manufacturer hired G&B Consulting to help them determine their best strategy.

This was potentially a very lucrative contract, and a high profile one too since the manufacturer is one of the biggest employers in the area. Therefore, several analysts at G&B Consulting, including you, were asked to tackle the problem independently to help ensure the best possible results. Before compiling a final report to give to the manufacturer, the results were presented to the project lead:

The first solution brought up was given by one of your coworkers. Using the manufacturer's projections of profits solely, he was able to create the following payoff matrix where each entry is in millions of dollars annually:

This coworker concluded that the dominant strategy for the manufacturer is to sue, and if the competitor assumed best play by the manufacturer, they would also sue.

Based only on the above payoff matrix, do you agree with the conclusion made by your coworker? Show all steps of finding any dominant strategies and Nash Equilibrium points.

The second solution was brought by a different coworker. She also created a payoff matrix for the scenario but did some independent research to estimate the competitor's profits in each outcome independent of the manufacturer's profits and came up with the following payoff matrix, again, the values represent millions of dollars in annual profits.

This coworker concludes that under these circumstances, the manufacturer should sue 50% of the time and not sue the other 50% of the time, and they should expect their competitor to do the same.

Based solely on this payoff matrix your coworker provided, do you agree with her conclusion? Show all steps of the mixed strategy algorithm to find the optimum strategy and explain if you do or do not agree with your coworker's results. Do you think this payoff matrix is a better representation of the scenario than the first one was? Explain why or why not.

You present your own solution that is based on a non-simultaneous game where the manufacturer first has to decide whether or not they wish to pursue litigation. If they do so choose, then their competitor will also have to decide if the wish to file a counter-suit. You utilized the same payoff matrix that the second coworker provided that contains information about both companies' projected profits, but then you created a game tree that excludes any non-credible threats. With this game tree, determine the optimum strategy. Show all steps of backwards induction and include any game trees used.

Create a PowerPoint presentation that shows all work, explanations, and responses detailed in the directions above that you will present to your interviewers.