This question is pertains to Nash Equilibria:
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.