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# Nash Equilibrium and Dominant Strategies

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I need some help with answering this problem:

Firm B
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?

https://brainmass.com/economics/game-theory/nash-equilibrium-dominant-strategies-477615

#### Solution Preview

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 ...

#### Solution Summary

Nash equilibrium and dominant strategies are examined.

\$2.19

## Strategy types are assessed. Identify the dominant strategy and Nash equilibrium

Scenario A Consider the following game: Payoffs are in millions of dollars.
Camden Inc.
Put Poison Pill
In Turbo Tech Dump Cash Assets
of Zamboni Tech
ABC Corporation Buy Turbo Tech -\$100, -\$1 \$2, -\$0.5
Buy Zamboni Tech 1, -\$1 -\$0.5, -\$0.5

.In the game in Scenario A, what is the Nash equilibrium?
(Points : 3)

The strategy pair associated with -\$100, -\$1.

The strategy pair associated with \$2, -\$.5.

The strategy pair associated with \$1, -\$1.

The strategy pair associated with -\$.5, -\$.5.

There is no Nash equilibrium in pure strategies.

6. Scenario CC Consider the following game:
It costs each firm Brokely \$3,000 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is \$2000 times the number of polluting firms.
Avale, Corp.
Pollute Donâ??t Pollute
Burgess, Inc. Pollute -\$4,000, -\$4,000 -\$2,000, -\$5,000
Donâ??t Pollute -\$5,000, -\$2,000 -\$3,000, -\$3,000

What is true about dominant strategies in the game in Scenario CC?

"Pollute" is a dominant strategy for both firms.

"Pollute" is a dominant strategy for Burgess only.

"Don't Pollute" is a dominant strategy for both firms.

"Don't Pollute" is a dominant strategy for Burgess only.

There are no dominant strategies.

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