Deliverable 04 Worksheet 1 Market Research Has Determ 968840
Deliverable 04 Worksheet1 Market Research Has Determined The Follow
Deliverable 04 – Worksheet 1. Market research has determined the following changes in market shares based on the different combinations of music choices for the two clubs: if both clubs play country, the new club (Club 1) does very well with a 24% increase in market share. If Club 1 plays country and the competing club (Club 2) plays rock, Club 2 gets a 12% increase in market share. If these choices are reversed, Club 2 does even better and gets an 18% increase in the market share. Lastly, if both clubs play rock, Club 1 does better and gets a 6% increase in market share.
This results in the following payoff matrix:
- When both play country: (24, ?)
- When Club 1 plays country and Club 2 plays rock: (?, 12)
- When Club 1 plays rock and Club 2 plays country: (-18, ?)
- When both play rock: (?, 6)
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.
Use the payoff matrix from number 1 to determine the optimum strategy for Club 1. Show all of your work. Enter your step-by-step answer and explanations here.
Use the payoff matrix from number 1 to determine the optimum strategy for Club 2. Show all of your work. Enter your step-by-step answer and explanations here.
Find and interpret the value of the game. Enter your step-by-step answer and explanations here.
Working in parallel, your coworker wants to make the recommendation that the new club owner should always follow the schedule shown below. Do you agree or disagree with this strategy? Explain your reasoning. Enter your step-by-step answer and explanations here.
Paper For Above instruction
Introduction
Market research provides critical insights into game theory strategies related to the music choices of competing clubs. By analyzing the payoff matrix and conducting strategic evaluations, club managers can optimize their decision-making to maximize market share. This paper systematically examines the presence of dominant strategies, identifies Nash equilibria, determines optimal strategies for each club, interprets the value of the game, and evaluates the implications of following a fixed schedule.
Analysis of Market Share Payoff Matrix
The payoff matrix exhibits the market share outcomes resulting from different music choices: country or rock. For clarity, the unfinished data refers to the market share increases for Club 2. Assuming the matrix is as follows:
| | Club 2: Country | Club 2: Rock |
|-------------|------------------|--------------|
| Club 1: Country | (24, 18) | (12, 6) |
| Club 1: Rock | (-18, 12) | (6, 6) |
This matrix indicates the payoffs for Club 1 and Club 2 in each scenario. The first value in each pair represents Club 1’s market share increase, and the second reflects Club 2’s increase.
Identification of Dominant Strategies
A dominant strategy exists if a player prefers a specific action regardless of what the opponent chooses.
- For Club 1:
- If Club 2 plays country:
- Playing country yields 24, playing rock yields -18; preference: country.
- If Club 2 plays rock:
- Playing country yields 12, playing rock yields 6; preference: country.
Since Club 1 prefers playing country in both scenarios, playing country is a dominant strategy for Club 1.
- For Club 2:
- If Club 1 plays country:
- Playing country yields 18, playing rock yields 12; preference: country.
- If Club 1 plays rock:
- Playing country yields 12, playing rock yields 6; preference: country.
Here, Club 2 prefers playing country regardless of Club 1’s choice. Thus, playing country is a dominant strategy for Club 2.
Conclusion: Both clubs have dominant strategies to play country.
Identification of Nash Equilibrium
A Nash equilibrium occurs where each player's strategy is optimal, given the opponent's choice.
- Since both players prefer to play country regardless of the other's choice, the strategy profile (Country, Country) is a Nash equilibrium.
Why? Because neither club gains by unilaterally changing their decision:
- If Club 1 switches to rock when Club 2 plays country, it would get -18, worse than 24.
- If Club 2 switches to rock when Club 1 plays country, it would get 12, worse than 18.
Thus, the Nash equilibrium is at (Country, Country) with payoffs (24, 18).
Optimal Strategies for Each Club
Given the dominant strategies identified:
- For Club 1, the optimal choice is to always play Country.
- For Club 2, the optimal choice is also to always play Country.
These choices maximize each club’s market share increase based on the payoff matrix. The equilibrium outcome (Country, Country) yields the highest joint payoff (24, 18).
Interpretation of the Game’s Value
The value of the game corresponds to the payoff at the equilibrium point. For the equilibrium (Country, Country), the payoffs are:
- Club 1: 24%
- Club 2: 18%
The value of the game from Club 1's perspective is 24% market share increase, representing the maximum guaranteed gain regardless of opponent’s strategies due to the dominant strategy.
Implication: Both clubs should stick with playing country to secure their respective market benefits. The outcome favors the club choosing the dominant strategies, corroborating the stability of the equilibrium.
Assessment of the Fixed Schedule Recommendation
The coworker’s suggested schedule involves a weekly pattern: Wednesday (Country), Thursday (Rock), Friday (Country), Saturday (Rock), Sunday (Country). This schedule alternates music genres, possibly aiming to attract different customer segments on different days.
Analysis:
- From a game-theoretic standpoint, sticking with dominant strategies simplifies decision-making but may not maximize revenue in dynamic contexts.
- The schedule's alternating nature might introduce variability that benefits only if customer preferences align with the schedule.
- Given that the analysis suggests both clubs benefit most by consistently playing country, a fixed schedule with mixed genres could dilute the advantages gained from the dominant strategy.
Conclusion:
I disagree with the recommendation to always follow the proposed schedule. Consistency in playing country, aligning with the dominant strategy, appears optimal. Fluctuating between genres might undermine market share gains and introduce instability, especially if customer preferences favor steady genre choices.
Conclusion
In strategic competition between clubs, analyzing payoff matrices reveals that both clubs have dominant strategies favoring playing country. The Nash equilibrium at (Country, Country) provides the most beneficial and stable outcome. While fixed scheduling may seem appealing for variety, the game-theoretic analysis advocates for consistency aligned with dominant strategies to maximize market share and minimize potential losses. Managers should prioritize strategies backed by such analyses for effective decision-making.
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