# Nash Equilibrium and Dominant Strategies

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?

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.

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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