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# Game Theory - Identify dominant strategy & Nash equilibrium

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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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https://brainmass.com/economics/game-theory/game-theory-identify-dominant-strategy-nash-equilibrium-377245

#### Solution Preview

See the attached file. Thanks

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 ...

#### Solution Summary

This post answers two multiple choice questions on game theory - one on identifying nash equilibrium and one on identifying dominant strategy

\$2.19
See Also This Related BrainMass Solution

## In choosing whether to deliver to six or seven neighborhoods, Pizza Spinners has to take into account not only its own costs, but also the delivery area response of its competitor Harry's Pizzeria.

Hello,

Please review attached document. I need help with this questions, I am finding it hard to solve the game theory questions.

Thanks in advance
Jummy

Game Theory

1a. In choosing whether to deliver to six or seven neighborhoods, Pizza Spinners has to take into account not only its own costs, but also the delivery area response of its competitor Harry's Pizzeria. If the payoffs per week from delivering in six and seven neighborhoods are as displayed in the Exhibit, what will Pizza Spinner's choose to do? (Note: Payoffs in the upper right corner go to Pizza Spinners and payoffs in the lower left go to Harry's).

PIZZA SPINNERS' CHOICE
SIX SEVEN
Harry's \$550 \$750
SIX \$700 \$100

Harry's \$120 \$370
SEVEN \$640 \$350
a. Serve six neighborhoods
B.Serve seven neighborhoods
C.Pizza Spinner will flip a coin because there is no clearly advantageous choice based on the data at hand
D.Pizza Spinner should hire Accenture to perform a year long study to produce a five year stategy to completely destroy Harry's Pizza.

b. What will Harry do?
a. Serve six neighborhoods
B.Serve seven neighborhoods
c.Buy out Pizza Spinner's, shut it down and eliminate the competition
d.Hire a hit man to kill the owner of Pizza Spinner's before Accenture can deliver its report

c. Given your answers to questions 1 and 2 above, is your selected solution an equilibrium?
a. No
b. Yes
c. Can't tell
d. There is no equilibrium in this case

d. If you said Yes in 3 above, what kind of equilibrium is this?
a.This question is irrelevant because the solution is not an equilibrium
b.A Nash equilibium
c.A maximax equilibrium
d.A maximin equilibium

e. If you think there is an equilibrium for this situation, what is the resulting payoff for Harry's and Pizza Spinners'? Ignore the absence of a \$ sign.
a.Harry's = 700; PS = 550
b.Harry's = 350; PS = 370
c.Harry's = 640; PS = 120
d.There is no equilibrium

f. Which, if either, of these pizzeria's has a dominant strategy or do both have dominant strategy?
a.Neither has a dominant strategy
b.Harry's selected strategy is dominant while Pizza Spinners' is dependent on Harry's choice
c.Both have a dominant strategy which results in the final solution
d.Pizza Spinner's strategy is dominant while Harry has no dominant strategy

2a. If the city-pair route from Orlando to New Orleans is served by only two air carriers, Northwest and Delta, and if the payoffs from discounting or maintaining high prices are as below, what behavior would you predict for Delta in a one-play game?

DELTA'S CHOICES
MAINTAIN DISCOUNT
Northwest's \$26,000 \$32,000
MAINTAIN \$24,000 \$18,000

Northwest's \$21,000 \$16,000
DISCOUNT \$28,000 \$12,000

a. Delta will select Discount because it has the highest payoff
b. Delta will select Maintain because, even if Northwest discounts, Delta is still better off
c. Delta has no dominant strategy so it has no clear choice for the one-play scenario
d. Delta decides to exit this city-pair market because the payoff matrix is just too difficult to solve

b. What will Northwest do?
a.Northwest will discount because that is the best payoff
b.Northwest will maintain because, even if Delta discounts, that gives it the best payoff
c.Northwest has no dominant strategy so it has no clear choice for the one-play scenario
d.Northwest decides to hire a team of private investigators to determine what Delta is doing to create this screwed up payoff matrix

c. How many Nash equilibria are present in the one-play scenario considering both Delta and Northwest?
a.2
b.4
c.6
d.None

d. Is there a mixed or randomized pricing strategy here for Delta among its Nash equilibria?
a.Yes
b.No
c.Yes, but it is not among the Nash equilibria
d.There is no such thing as a mixed or randomized pricing strategy in game theory

e. Is there a mixed or randomized pricing strategy among Northwest's Nash equilibria?
a. I already told you there is no mixed or randomized pricing strategy in game theory - how about asking a relevant question for a change.
b. Yes
c. No
d. Since there is a mixed/randomized pricing strategy for Delta, there can't be one for Northwest - only one per payoff matrix

3a. Retailers A and B face the following payoff matrix. Is there a dominant strategy for A in a one-play scenario?

STORE A's CHOICES
MAINTAIN DISCOUNT
STORE B \$550 \$950
MAINTAIN \$700 \$100

STORE B \$120 \$370
DISCOUNT \$640 \$350
a.Yes
b.No
c.Maybe
d.Only if the Congress intervenes and passes laws regulating retailer's pricing behavior

b. Is there is a dominant strategy for A in the one-play scenario what is it?
a.There is no dominant strategy
b.Maintain
c.Discount
d.Have a sit down with Retainer B and conspire to set prices so they don't have to worry about this competition any longer

c. Is there a dominant strategy for Retailer B in the one-play scenario?
a.Retailers never have a dominant strategy in any scenario
b.No
c.Yes
d.Not enough information to determine

d. What is the dominant strategy for Retailer B in the one-play scenario?
a.Retailer B has no dominant strategy in the one-play scenario
b.Discount
c.Maintain
d.For Retailer B the concept of a dominant strategy is undefined

e. Is there a cooperation solution, if we allow multiple iterations of the game, that can make both retailers better off?
a.No
b.Yes
c.There is no such thing as cooperation solution in game theory
d.Not enough information to determine

f. What is the coorperation solution, if there is one?
a.There is not cooperation solution
b.Both retailers will discount
c.Both retailers will maintain
d.Not enough information to determine

4a. Suppose a new low cost discount firm must decide in advance between introducing LARGE or SMALL capacity in a licensed cable TV market where the incumbent then will decide on a HIGH or MATCHING pricing response. If the following table describes the payoffs from various combinations of these strategies, what capacity will the new entrant choose?

Incumbent Profit Entrant Profit

With LARGE Capacity HIGH Prices \$50 \$10
MATCHing Prices \$70 \$3

With SMALL Capacity HIGH Prices \$90 \$5
MATCHing Prices \$60 \$1
a.Small
b.Large
c.Not enough information to determine
d.Depends on the phase of the moon and whether Jupiter is in retrograde.

b. Is there a cooperation solution that can make them both better off?
a. No
b.Yes
c.Not enough information to determine
d.Yes, but the local authorities won't let them achieve it

c. Is the solution in this case a Nash equilibrium?
a.No
b.There is a solution in this case but it is not an equilibrium
c.Yes
d.Not enough information to determine

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