Nash Equilibria Analysis

 
Instructions
A local law firm has hired G & B Consulting to help determine a business strategy. There is a competing firm in the area as well, and the first firm suspects that they are also reconsidering their business strategy by going to a different consulting firm. The choice that each firm is faced with is whether or not to lower their rates to attract more customers. If neither company changes prices, both firms continue to make a profit. If one prices low while the other does not, the firm that prices low will take all of the business. If both firms price low, they will continue to split the market, but at reduced profits. More specifically, if both firms price high, they each can expect yearly profits of $15 million. If Firm 1 prices high while Firm 2 prices low, Firm 1 should only expect profits of $5 million while Firm 2 should expect profits of $25 million. If they choose the reverse, the payoffs would be switched accordingly. If both firms choose to price low, they should both expect profits of $5 million.
Part 1: You decide to develop your strategy by creating a payoff matrix for this scenario and finding any pure strategy equilibriums that exist. Write up a detailed solution on finding the pure strategy equilibriums, and include the payoff matrix you created that will be added to the final report to be delivered to the client.
Part 2: Your coworker who is also working on this project wants to advise the firm that they should price low no matter what, as it will give the chance of obtaining the highest profits. The two of you need to determine whose strategy is better and why before bringing your analysis to the client. Compose an email to your coworker that explains which solution you would choose and why you would choose it, along with any reason for disregarding either solution.
Part 3: Create a report that details how you would advise the firm. Be sure it includes all of the relevant technical information you used to reach your conclusion, as well as a plainly stated strategy that you advise.

Requirements:
– Communication about the problem was very constructive and professional. Strategy was fully explained. A thorough explanation for how to obtain the highest profits was stated
– mostly clear and understandable. Most of the components are addressed.The written report is clear and understandable. All components thoroughly addressed.
– The math calculations for payoff matrix are all correct. All work shown is correct, or with minor errors.