Deliverable 03 Worksheet 1: Market Research Has Determined E

Deliverable 03 Worksheet1 Market Research Has Determined Estimates

Deliverable 03 – Worksheet 1. Market research has determined estimates for each law firm’s expected profits for the various outcomes of this scenario. If both firms agree to the merger then each should individually expect a profit of 16 million in the next year. If our client agrees to the merger while the competitor does not, our client would expect profits of 8 million in the next year while the competitor would expect profits of 15 million. If the decisions were reversed then the payouts would also be reversed. If neither firm agrees to the merger then both would expect profits of 12 million in the next year. Construct a payoff matrix to represent the profits (in millions of dollars) for each firm under the different outcomes. Enter your step-by-step answer and explanations here. 2. Use the payoff matrix from number 1 to determine if a dominant strategy exists for either firm. Show all of your work. Enter your step-by-step answer and explanations here. 3. Use the payoff matrix from number 1 to determine any Nash equilibrium points. Show all of your work. Enter your step-by-step answer and explanations here. 4. Explain your recommendation to the client, citing your work from number 2 and number 3. Enter your step-by-step answer and explanations here. 5. Working in parallel your co-worker wants to make the recommendation that the client should agree to 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. Enter your step-by-step answer and explanations here.

Paper For Above instruction

The scenario presented involves two law firms contemplating a merger, with payoffs dependent on whether each firm agrees or declines. Analyzing such situations involves constructing a payoff matrix, identifying dominant strategies, and determining Nash equilibria, which are essential concepts in game theory. This analysis will guide strategic decision-making, helping the client understand the best course of action based on rational behavior of competitors.

Constructing the Payoff Matrix

The first step is to create a matrix depicting the possible outcomes and profits for each firm. The four scenarios are:

• Both firms agree to the merger
• Our client agrees, but the competitor declines
• The competitor agrees, but our client declines
• Neither firm agrees to the merger

Based on the given data, the profits are as follows:

• Both agree: (16, 16)
• Client agrees, competitor declines: (8, 15)
• Client declines, competitor agrees: (15, 8)
• Both decline: (12, 12)

Arranged as a payoff matrix:

Identifying Dominant Strategies

A dominant strategy is one that yields the highest payoff regardless of the opponent's action. For each firm, we analyze whether such strategies exist by comparing payoffs across the matrix.

For the client:

• If the competitor agrees:
• Client's options: Agree (16), Decline (15). The client prefers to agree.
• If the competitor declines:
• Client's options: Agree (8), Decline (12). The client prefers to decline.

For the competitor:

• If the client agrees:
• Competitor's options: Agree (16), Decline (15). The competitor prefers to agree.
• If the client declines:
• Competitor's options: Agree (8), Decline (12). The competitor prefers to decline.

Conclusion: Neither firm has a dominant strategy because their optimal choice depends on the other firm's decision. The client prefers to agree only if the competitor agrees, and declines if the competitor declines. Same applies for the competitor.

Determining Nash Equilibria

A Nash equilibrium occurs when neither firm can improve their payoff by unilaterally changing their strategy. From the matrix, the potential equilibria are:

• (Agree, Agree): both get 16 — both have no incentive to deviate, since switching would reduce their payoff.
• (Decline, Decline): both get 12 — neither gains by unilateral deviation, as switching would change their payoff to 15 (if one deviates to agree while the other declines, the deviator gets 8 or 15 respectively).

Therefore, the two Nash equilibria are (Agree, Agree) and (Decline, Decline).

Strategic Recommendations

Given the coexistence of two Nash equilibria, the optimal choice depends on the client's risk preferences and strategic considerations. The (Agree, Agree) equilibrium yields the highest joint payoff (16, 16), favoring cooperation. However, the (Decline, Decline) equilibrium is more conservative, with both firms settling for moderate profits (12).

My recommendation is to aim for the (Agree, Agree) scenario, as it maximizes profits and fosters firm collaboration. Nonetheless, the client should consider the likelihood of the competitor’s response and the potential benefits of cooperation versus defection based on their strategic priorities.

Assessment of the "Always Agree" Strategy

My co-worker’s suggestion that the client should agree to the merger regardless of the competitor’s decision assumes that this guarantees the highest profits. However, analysis shows that if the client always chooses to agree, the profits are (16 if the competitor agrees, 8 if the competitor declines).

From a rational standpoint, blindly agreeing in all scenarios neglects the potential for better individual outcomes when the competitor declines—namely avoiding an expected profit of only 8 when the client unilaterally agrees if the competitor declines.

Therefore, I disagree with the strategy of always agreeing, because it exposes the client to asymmetric risks and suboptimal payoffs when the competitor declines. Strategic decision-making should weigh the likelihood of competitor responses and the overall profitability, aligning with game theory principles to optimize outcomes.

Conclusion

Effective analysis of the merger scenario through payoff matrices, dominant strategies, and Nash equilibria reveals that mutual agreement can lead to optimal profits. However, the absence of a dominant strategy means the client must consider their risk tolerance and expectations of the competitor’s behavior. Formulating a policy of conditional cooperation—where agreement is contingent upon the competitor’s actions—can maximize strategic benefits. The approach underscores the importance of game theory in guiding corporate strategic decisions, especially in merger negotiations.

References

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• Myerson, R. B. (1997). Game Theory: Analysis of Conflict. Harvard University Press.
• Osborne, M. J. (2004). An Introduction to Game Theory. Oxford University Press.
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• Luce, R. D., & Raiffa, H. (1957). Games and Decisions. Wiley.
• Zermelo, E. (1913). Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. Proceedings of the Fifth Congress of Mathematicians.
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