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Nastasia
25 days ago
10

Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide

upon the size of their research budget: Synergy's Decision Large Budget Small Budget Dynaco's Decision Large Budget $20 million, $25 million $15 million, $0 Small Budget $0, $60 million $25 million, $30 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy a dominant strategy. If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco a dominant strategy. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.) True False
Business
1 answer:
Mariulka [3.1K]25 days ago
7 0

Answer:

Explanation:

Synergy's Choices Large Budget Small Budget Dynaco's Choices Large Budget $20 million, $25 million $15 million, $0 Small Budget $0, $60 million $25 million, $30 million If Synergy assumes

If Synergy presumes Dynaco will opt for a large budget, then Synergy should also select a large budget.

If Synergy thinks Dynaco will choose a small budget, Synergy should still go for a large budget.

This indicates that Synergy indeed has a dominant strategy.

If Dynaco believes Synergy will pursue a large budget, it will likewise pursue a large budget.

Conversely, if Dynaco believes that Synergy will choose a small budget, it will choose a small budget as well.

Therefore, Dynaco lacks a dominant strategy.

Correctly stated, the Nash equilibrium is found at (large budget, large budget).

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Utilizing Chebyshev’s Theorem is key.

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Chebyshev's Theorem states that at least 1−1/k² of the data falls within k standard deviations from the mean.

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According to Chebyshev’s Theorem, at least 1−1/k² of the data is within k standard deviations from the mean. Setting k = 4 gives us:

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