Construct A Payoff Matrix For The Merger Decision And Analyz

Construct a payoff matrix for the merger decision and analyze strategic options

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 regarding a merger. The merger would result in more shared resources and greater efficiency. However, it would require a committed effort to succeed. An analysis has provided the following profit expectations: if both firms agree to the merger, each can expect profits of $30 million next year; if neither agrees, each expects $15 million; if one pursues the merger while the other does not, the pursuing firm expects $10 million, and the other expects $20 million. You are tasked with constructing a payoff matrix, analyzing for dominant strategies and Nash Equilibrium points, and advising on the best course of action. Additionally, you will review a coworker's recommendation to pursue the merger regardless of the other firm's decision.

Paper For Above instruction

To analyze the strategic interactions between the two competing law firms regarding the potential merger, it is essential to model their choices using a payoff matrix. This approach allows the visualization of possible outcomes and the strategic decisions each firm might take based on their expectations and incentives.

Constructing the Payoff Matrix

The first step involves identifying the decision options available to each firm. Each firm has two choices: to pursue the merger (merger) or not (no merger). The possible outcome combinations are therefore four: both pursue, neither pursue, one pursues while the other does not, and vice versa.

The payoff matrix can be organized as follows, with the firm's choices as rows and columns:

| | Firm B: Merger | Firm B: No Merger |

|--------------------|------------------|-------------------|

| Firm A: Merger | (30, 30) | (10, 20) |

| Firm A: No Merger | (20, 10) | (15, 15) |

In this matrix, the first number in each pair indicates Firm A’s profit; the second number indicates Firm B’s profit, reflecting the profit expectations under each scenario.

Analysis for Dominant Strategies

A dominant strategy exists for a player if choosing that strategy yields a higher payoff regardless of the other firm's choice.

- For Firm A:

- If Firm B chooses "Merger," Firm A’s payoff is:

- Merger: $30 million

- No Merger: $20 million

- Here, "Merger" yields a higher payoff.

- If Firm B chooses "No Merger," Firm A’s payoff is:

- Merger: $10 million

- No Merger: $15 million

- Here, "No Merger" yields a higher payoff.

- For Firm B:

- If Firm A chooses "Merger," Firm B’s payoff is:

- Merger: $30 million

- No Merger: $10 million

- "Merger" yields a higher payoff.

- If Firm A chooses "No Merger," Firm B’s payoff is:

- Merger: $20 million

- No Merger: $15 million

- "Merger" again yields a higher payoff.

Thus, firm B will prefer to pursue the merger regardless of Firm A’s choice because the payoff from "Merger" is higher in every case. Firm A prefers "Merger" if Firm B chooses "Merger" but prefers "No Merger" if Firm B does not pursue the merger. Therefore, Firm A does not have a dominant strategy because its optimal choice depends on Firm B's decision.

Identifying Nash Equilibrium

A Nash Equilibrium occurs when neither firm can improve their payoff by unilaterally changing their decision, given the other firm's choice.

- Scenario 1: Both pursue the merger (30, 30):

- Firm A cannot increase profit by switching alone because switching to "No Merger" would drop its profit from $30 million to $20 million, given Firm B's decision.

- Firm B cannot increase profit by switching alone because switching to "No Merger" would reduce its profit from $30 million to $10 million.

- Result: Both firms' choices are mutually best responses, indicating a Nash Equilibrium.

- Scenario 2: Both do not pursue the merger (15, 15):

- If either firm switches to "Merger," their profit would increase to $20 million (for the firm switching), but the other’s payoff would decrease to $10 million.

- Given this, neither firm would want to deviate unilaterally, indicating a second Nash Equilibrium at (No Merger, No Merger).

In conclusion, there are two Nash Equilibria: one where both pursue the merger and one where neither does.

Implications for the Client

The presence of multiple Nash Equilibria introduces strategic considerations for the client. The firm must consider the likely behavior of the competitor and weigh the benefits of pursuing the merger amidst the potential outcomes.

- Pursuing the merger could be advantageous if the firm believes the competitor will also pursue it, leading to a profitable outcome of $30 million.

- However, if the firm fears the competitor will not pursue the merger, choosing "No Merger" might avoid the risk of a lower payoff ($10 million).

This strategical information suggests that the decision hinges upon expectations about the competitor’s actions. A cautious approach might favor the status quo unless there is confidence the merger will be reciprocated.

Assessment of the Coworker’s Recommendation

The coworker advocates pursuing the merger regardless of the other firm's decision, asserting it presents the opportunity for the highest profits ($30 million). While pursuing the merger unilaterally does yield the highest payoff for the firm if the other does not reciprocate, this approach ignores the possibility of being in a less favorable position if the other firm abstains. In game theory, this is akin to a "commitment" strategy that might be risky without assurances the competitor will behave similarly.

Given the payoff structure, the strategy makes sense only if the firm can influence or ensure the other’s cooperation, such as through negotiations or incentives. Otherwise, blindly pursuing the merger could result in lower profits (e.g., $10 million if the other does not pursue), highlighting the importance of strategic communication and credible commitments. Therefore, I do not fully agree with the coworker’s blanket recommendation; instead, a strategic assessment should consider the likelihood of the competitor’s response and potential risks.

Conclusion

Constructing and analyzing the payoff matrix reveals two Nash Equilibria: both firms pursue the merger or both abstain. The existence of these equilibria indicates that strategic stability exists in these outcomes. The firm’s decision should be informed by expectations about the competitor’s actions and the potential for coordination. Pursuing the merger unilaterally might maximize profits if the other firm joins, but risky if the other maintains the status quo. Therefore, a nuanced strategy involving negotiations and credible commitments is advisable over a blind pursuit of the merger, aligning with game-theoretic insights about strategic interdependence and equilibrium stability.

References

• Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.
• Myerson, R. B. (2013). Game Theory. Harvard University Press.
• Osborne, M. J., & Rubinstein, A. (1994). A Course in Game Theory. MIT Press.
• Raiffa, H., & Richardson, J. (1991). Delegation and strategic decision-making. Journal of Public Economics.
• Schelling, T. C. (1960). The Strategy of Conflict. Harvard University Press.
• Tadelis, S. (2013). Game Theory: An Introduction. Princeton University Press.
• von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
• Bernheim, B., & Rangel, A. (2009). Beyond Revealed Preference: Choice-Theoretic Foundations for Behavioral Welfare Economics. The American Economic Review.
• Grossman, G. M., & Helpman, E. (1994). Protection for Sale. The American Economic Review.
• Neilson, W. S., & Resnick, S. (2009). Game Theory and Business Strategy. Routledge.