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Nash Equilibrium and Dominant Strategies

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I need some help with answering this problem:

Firm B
Strategy Advertise Don't Advertise
Firm A Advertise $4,$4 $20, $1
Don't Advertise $1, 20 $10, $10

A. Does anyone have a dominant strategy?
B. What is the Nash Equilibrium?
C. What is the socially optimal solution (at what point is total profit maximized)?
D. How would a negotiated solution lead to this socially optimal solution?
E. If you had to call in a mediator to negotiate this socially optimal solution, how much would they charge and why?

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Solution Summary

Nash equilibrium and dominant strategies are examined.

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This is a somewhat classic Game Theory problem:

A. Firstly, the concept of dominant strategies has been raised. A weakly dominant strategy is at least as good in most contingencies, and better in one contingency. A strictly dominant strategy is better in all contingencies. Lets look at the payoffs:

Firm A appears to have a dominant strategy (advertise). Consider where Firm B decides to ...

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