Nash Equilibria Analysis

 
A local law firm has hired G&B Consulting to help determine a business strategy. There is a competing firm in the area and recently the two firms have begun talks in regards to a merger. The merger would mean that there are now more shared resources than either had before individually, and they would operate more efficiently. However, it would take a committed effort to pull it off. One of your coworkers analyzes the expected profits of each firm should they choose to go along with the merger or not and gives you the following results. If both firms agree to the merger the new firm should expect profits of $30 million in the next year. If neither firm agrees to the merger then each should expect profits of $15 million for the next year. If one firm spends resources on pursuing the merger while the other does not, the firm pursuing the merger should expect profits of $10 million the next year while the other firm is able to focus more on new clients and should expect profits of $20 million in the next year.
Construct a payoff matrix to represent the profits for each company under the different outcomes. Then, determine if any dominant strategies exists and explain how you are able to determine this. Identify any Nash Equilibrium points. Use these to explain the options available to the client.
A coworker who is also working on the project used the same information you were given and wants to advise the client to work towards the merger no matter what as it will give the chance of obtaining the highest profits. Do you agree with this strategy?  Explain why or why not.
Create a report using Microsoft Word that will detail your responses to the client. Show all work, including any payoff matrices used, all steps to determine if there is a dominant strategy, all steps used to find any Nash Equilibrium points, and any necessary explanations with your solutions.
In the same document, compose an email in response to your coworker’s results.

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