Deliverable 05 Worksheet 1 Market Research Determined

Deliverable 05 Worksheet1 Market Research Has Determined The Follow

Deliverable 05 – Worksheet 1. Market research has determined the following changes in the polls based on the different combinations of choices for the two candidates on the tax bill in the upcoming debate: Incumbent Challenger Stay Break Stay (0, , 0) Break (1, , 3) Use this payoff matrix to determine if there are dominant strategies for either player. Find any Nash equilibrium points. Show all of your work. Enter your step-by-step answer and explanations here. 2. Use the payoff matrix from number 1 to determine the optimum strategy for your client (the challenger). Show all of your work. Enter your step-by-step answer and explanations here. 3. Use the payoff matrix from number 1 to determine the optimum strategy for the incumbent. Show all of your work. Enter your step-by-step answer and explanations here. 4. Knowing that flip-flopping on an issue is worse than taking a stand on either side, you must recommend a single strategy to the client to take in the upcoming debate. Take into account the predictability of the incumbent’s strategy and assume rationality by both players. Enter your step-by-step answer and explanations here. 5. Working in parallel your co-worker finds that there is a 60% chance that the incumbent will choose to stay within party lines. Does this agree with your findings? If not, identify the error made by your co-worker. Enter your step-by-step answer and explanations here.

Sample Paper For Above instruction

The analysis of strategic decision-making in political debates requires understanding the interactions between candidates’ choices and their associated payoffs. Utilizing game theory, particularly payoff matrices, provides a clear framework for evaluating strategies, identifying equilibrium points, and making optimal decisions based on rationality assumptions. This paper examines a specific payoff matrix involving two candidates — the incumbent and the challenger — and explores their strategic options regarding their stance on a tax bill debate.

The provided payoff matrix is as follows:

This matrix indicates the payoffs for each player based on their combined strategic choices. The first number in each pair represents the incumbent's payoff, and the second corresponds to the challenger's payoff.

Analysis of Dominant Strategies and Nash Equilibria

A dominant strategy exists when a player's choice yields a higher payoff regardless of the opponent's decision. For the incumbent, comparing payoffs:

• If the challenger stays, the incumbent's options are stay (0) or break (0); neither provides a strictly higher payoff, so no dominant strategy here.
• If the challenger breaks, the incumbent's options are stay (1) or break (3). In this case, breaking yields a higher payoff (3) compared to staying (1); thus, breaking is dominant for the incumbent.

Similarly, for the challenger:

• If the incumbent stays, challenger payoff for stay is 0, for break is 3; breaking is better.
• If the incumbent breaks, challenger payoff for stay is 0, for break is 1; staying yields a higher payoff, so staying is better.

From this, it’s clear the challenger prefers to stay if the incumbent breaks, and the incumbent prefers to break if the challenger stays. The strategy profile (Break, Stay) yields payoffs (3, 0). However, because the challenger prefers to stay when the incumbent breaks, and vice versa, no pure strategy dominant strategy exists for both players simultaneously.

Identification of Nash Equilibria

A Nash equilibrium occurs when neither player can improve their payoff by unilaterally changing strategies. Analyzing the payoff pairs:

• (Stay, Stay): Both get 0. The challenger can improve by switching to break (payoff 3), so not a NE.
• (Stay, Break): Payoffs (1, 3). The incumbent could improve by switching to break (payoff 3); thus, not a NE.
• (Break, Stay): Payoffs (3, 0). The challenger has an incentive to switch to stay (payoff 0), so not a NE.
• (Break, Break): Payoffs (0, 1). The incumbent could improve by switching to stay (payoff 1); thus, not a NE.

However, the analysis suggests that the strategic interaction may settle around the point where players are indifferent. Given the payoffs, the only stable point is when the incumbent breaks and the challenger stays, which yields (3, 0) but is not a mutual best response. Therefore, the game highlights strategic tension with no pure strategy stable equilibrium, but mixed strategies could be explored further.

Optimal Strategies for the Challenger and Incumbent

The challenger’s best response depends on the incumbent’s choice. If the incumbent stays, the challenger should stay (payoff 0 vs. 3), but since 3 > 0, actually, the challenger prefers to break if the incumbent stays, which contradicts the previous statement. Correctly reviewing, the challenger prefers to break when the incumbent stays (payoff 3 versus 0), indicating breaking is better if the incumbent stays. When the incumbent breaks, challenger prefers to stay (payoff 0) over breaking (payoff 1); so, the challenger’s best response varies depending on the incumbent’s choice.

Similarly, the incumbent prefers to break if the challenger stays, but prefers to stay if the challenger breaks. These response patterns help determine the best strategies, with the game being potentially dynamic or requiring mixed strategies for equilibrium.

Recommended Strategy and Predictability

Considering the analysis, the best strategy for the challenger is to break if the incumbent stays, aligning with the dominant response, and to stay if the incumbent breaks, avoiding the worst outcome. Given rationality and assuming the incumbent’s strategic behavior is predictable, the challenger should adopt a mixed strategy balancing these responses. The incumbent, recognizing the challenge, should consider that their best reply might be to break, especially if they predict the challenger’s behavior.

Impact of Probabilistic Incumbent Behavior

The co-worker's assertion that there is a 60% chance the incumbent will stay within party lines reflects a probabilistic estimate of the incumbent's strategy. Comparing this with the previous analysis, if the dominant strategy for the incumbent is to break (as indicated by higher payoffs in certain scenarios), a 60% chance of staying suggests the risk of misprediction or other external influences not captured in the payoff matrix. There could be a discrepancy indicating an error in assumptions about the incumbent’s strategic preferences or the interpretation of payoffs. The primary error might be assuming deterministic behavior when, in reality, there is a probabilistic mix, or it could signal that the payoff matrix does not fully reflect the incumbent's strategic preferences.

Conclusion

This analysis emphasizes the importance of strategic thinking in political decision-making, illustrating how payoff matrices can identify dominant strategies and Nash equilibria. The challenger’s optimal response involves carefully balancing risks, while the incumbent’s strategy may be influenced by expectations of the challenger’s moves. Probabilistic assessments, such as the co-worker’s estimate, require consistency with payoff structures and rationality assumptions to inform effective strategy recommendations.

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