Deliverable 04 Worksheet 1 Market Research Has Determ 786633
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:
| | Club 2: Country | Club 2: Rock |
|----------------|------------------|--------------|
| Club 1: Country | (24, –) | (12, –) |
| Club 1: Rock | (–18, –) | (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 co-worker 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.
Wednesday Thursday Friday Saturday Sunday
Country Rock Country Rock Country
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Paper For Above instruction
Introduction
Market competition strategies often involve analyzing payoffs based on different strategic choices, especially in scenarios where firms have conflicting interests but are interconnected through their decisions. The scenario presented involves two clubs competing based on their music choices—Country or Rock—and the consequent impact on their market share increases. The analysis involves assessing dominant strategies, identifying Nash equilibria, and recommending optimal strategies. Furthermore, evaluating the value of the game offers insight into the strategic advantage or overall payoff achievable in this competitive setup.
Analysis of the Payoff Matrix and Strategic Dominance
The payoff matrix given is:
| | Club 2: Country | Club 2: Rock |
|--------------|------------------|--------------|
| Club 1: Country | (24, –) | (12, –) |
| Club 1: Rock | (–18, –) | (6, –) |
Note: Since the payoff matrix presents values only for Club 1's gains, the minus signs indicate that the corresponding data for Club 2's payoffs should be considered as complementary or comparative. For clarity, we'll interpret the matrix as representing the increase in market share for each club, with the primary focus on identifying strategies.
Dominant Strategies
To find if either club has a dominant strategy, analyze each club's choices:
- For Club 1:
- If Club 2 chooses Country:
- Playing Country yields 24%, Rock yields –18%.
- Since 24 > –18, Club 1 prefers Country.
- If Club 2 chooses Rock:
- Playing Country yields 12%, Rock yields 6%.
- Since 12 > 6, Club 1 prefers Country.
Therefore, Club 1 has a dominant strategy: Play Country.
- For Club 2:
- When Club 1 plays Country:
- If Club 2 plays Country, the payoff is not explicitly given, but considering the pattern, the best response is the one maximizing their increase.
- When Club 1 plays Rock:
- Similarly, their preferred move can be inferred based on the context.
Given the incomplete data for Club 2, assuming symmetry, the dominant strategy for Club 2 can be inferred as playing Rock, especially considering that when Club 1 plays Rock, Club 2's payoffs are maximized if it plays Rock.
Nash Equilibrium Analysis
Nash equilibrium occurs where neither player would want to unilaterally change their strategy.
From the strategic consideration:
- If Club 1 chooses Country and Club 2 chooses Country:
- Club 1's payoff: 24
- Club 2's payoff: inferred similar positive value since their best responses align
- Alternatively, if Club 1 chooses Country and Club 2 chooses Rock:
- Club 1's payoff: 12
- Club 2's payoff: less favorable, suggesting not stable
Based on the dominant strategies, the likely Nash equilibrium is both clubs playing Country, with Club 1's market share increasing by 24%.
Interpretation of the Game's Value
The value of the game is approximated by the payoff at the equilibrium point—here, the two clubs choosing Country yields the highest payoff (24% increase for Club 1). This suggests that mutual cooperation or predictable strategies favor higher market shares when clubs settle into dominant strategies.
Optimal Strategies for Each Club
- For Club 1: The dominant strategy is to play Country, leading to maximum market share increase (24%) when Club 2's response is considered.
- For Club 2: The optimal strategy is to Play Rock, as this maximizes its market share increase (not explicitly quantified but inferred) and stabilizes the equilibrium.
Strategic Recommendations and Final Evaluation
The recommended approach is for both clubs to adopt their dominant strategies:
- Club 1 should always select Country.
- Club 2 should always select Rock.
This ensures stability and maximizes each club's market share increase given the strategic matrix. Deviating from these strategies could result in lower payoffs, making the dominant strategies the most logical choice.
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Conclusion
This analysis underscores the importance of identifying dominant strategies and equilibrium points in strategic decision-making within competitive markets. Given the payoff structure, the clubs benefit most by following their dominant strategies, with Club 1 playing Country and Club 2 playing Rock, resulting in optimal market share gains. Making strategic choices aligned with dominant strategies ensures predictable outcomes and maximizes benefits in competitive scenarios.
References
- Osborne, M. J. (2004). An Introduction to Game Theory. Oxford University Press.
- Myerson, R. B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.