Deliverable 05 Worksheet 1 Market Research Has Determined

Deliverable 05 Worksheet1 Market Research Has Determined The Follow

Determine if there are dominant strategies for either player based on the provided payoff matrix. Find any Nash equilibrium points, showing all work and explanations. Use the payoff matrix to decide the optimal strategy for the challenger and the incumbent, detailing all steps. Recommend a single strategy for the client considering the strategies’ predictability and rationality of both players. Analyze the co-worker's 60% chance assumption regarding the incumbent’s strategy, identify any errors, and explain whether it agrees with your findings.

Paper For Above instruction

The analysis of strategic decision-making in competitive environments often involves understanding the concepts of dominant strategies, Nash equilibria, and optimal strategies for involved players. The provided payoff matrix, which is partially specified with payoffs corresponding to different strategy combinations undertaken by the incumbent and challenger regarding the tax bill debate, serves as a foundation for such analysis. This paper systematically evaluates each component, beginning with identifying dominant strategies, moving toward equilibria, and culminating in strategic recommendations grounded in game theory principles.

Understanding the Payoff Matrix

For clarity, the payoff matrix indicates the incentives for both players based on their chosen strategies: "Stay" or "Break." Each cell in the matrix shows a pair of payoffs, with the first number representing the incumbent's outcome and the second the challenger's. Although the problem indicates incomplete data with placeholders, standard practice involves assuming specific numerical payoffs to analyze the strategic landscape effectively. For this analysis, we interpret the matrix as follows:

• When both stay, payoffs are (0, 0).
• When the incumbent stays and challenger breaks, payoffs are (0, 3).
• When the incumbent breaks and challenger stays, payoffs are (1, 0).
• When both break, payoffs are (3, 3).

This hypothetical structure allows us to explore how strategic choices impact each player's payoffs and determine optimal strategies accordingly.

Identifying Dominant Strategies

A dominant strategy for a player is one that yields a higher payoff regardless of the other player's choice. To determine if such strategies exist, each player's payoffs are compared across possible strategies.

For the incumbent:

• If challenger stays:
• Stay yields 0, break yields 1 → break dominates stay.
• If challenger breaks:
• Stay yields 0, break yields 3 → break dominates stay.

Since break yields a higher payoff for the incumbent in both scenarios, "Break" is the dominant strategy for the incumbent.

For the challenger:

• If incumbent stays:
• Stay yields 0, break yields 3 → break dominates stay.
• If incumbent breaks:
• Stay yields 0, break yields 3 → break dominates stay.

Similarly, "Break" is the dominant strategy for the challenger since it provides higher payoffs in all scenarios.

Finding Nash Equilibria

Game theory states that a Nash equilibrium occurs where neither player benefits from unilaterally changing their strategy. Given both players' dominance of the "Break" strategy, the cell where both choose to break, with payoffs (3, 3), constitutes a Nash equilibrium. Neither player gains by deviating from this choice, assuming rationality and complete information.

Determining Optimal Strategies for Each Player

Given the dominance of "Break" for both, the challenger’s optimal strategy is to break, aiming for the payoff of 3. For the incumbent, similarly, breaking is optimal due to the higher payoff regardless of the challenger’s move. These conclusions are consistent with game theory, wherein rational players gravitate toward dominant strategies leading to Nash equilibria.

Strategic Recommendation to the Client

Considering the analysis, the best strategy for the challenger in the upcoming debate is to "Break" on the tax bill. Rationality and the dominance of this strategy suggest that deviating would not improve the challenger's payoff. Furthermore, if the incumbent also chooses "Break," the challenger can anticipate a predictable response, which simplifies strategic planning. This approach minimizes the risk of unfavorable payoffs associated with flip-flopping and aligns with the principle that taking a clear stand is more advantageous than vacillating (Fudenberg & Tirole, 1991).

Analyzing the Co-worker's 60% Probability Estimate

The co-worker's assumption that there is a 60% chance the incumbent will stay within party lines contradicts the logical deduction from the payoff matrix, which indicates "Break" as the dominant strategy for the incumbent with a 100% rational payoff. This discrepancy suggests an error in their reasoning. They may have overlooked the dominance of "Break" or incorrectly interpreted the strategic incentives, perhaps considering external factors or uncertainties not reflected in the payoff matrix. If the incumbent acts rationally based on the payoffs, the probability of choosing "Stay" diminishes significantly, aligning closer to zero rather than 60%. Thus, the error lies in the misinterpretation of the rational strategic response indicated by game theory principles.

Conclusion

In conclusion, the strategic analysis reveals that both players have a dominant strategy to "Break," leading to a Nash equilibrium at (Break, Break). The challenger should adopt "Break" to maximize their payoff, and the incumbent is also best served by "Break" under rational decision-making. The co-worker's assumption about the 60% likelihood of staying within party lines is inconsistent with the dominance analysis, indicating a misjudgment of strategic incentives. Overall, the findings endorse adopting a clear, consistent stance to optimize strategic advantage in political negotiations concerning the tax bill debate, adhering to principles of game theory and rational choice.

References

• Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.
• Myerson, R. B. (1997). Game Theory: Analysis of Conflict. Harvard University Press.
• Osborne, M. J. (2004). An Introduction to Game Theory. Oxford University Press.
• Kreps, D. M. (1990). Corporate Culture and Economic Theory. In Perspectives on Positive Political Economy (pp. 90-143). Cambridge University Press.
• Rasmusen, E. (2001). Games and Information: An Introduction to Game Theory. Blackwell Publishing.
• Gintis, H. (2009). Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction. Princeton University Press.
• Dixit, A., & Nalebuff, B. (2008). The Art of Strategy: A Game Theorist's Guide. W.W. Norton & Company.
• Schelling, T. C. (1960). The Strategy of Conflict. Harvard University Press.
• Binmore, K. (2007). Playing for Real: A Text on Game Theory. Oxford University Press.
• Luce, R. D., & Raiffa, H. (1957). Games and Decisions. John Wiley & Sons.