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# dominant strategy in game theory

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1. In game theory analysis, what is a "dominant strategy"?

2. A firm's most recent annual dividend was \$2 per share; its shares sell for \$40 in the stock market, and the company expects its dividend to grow at a constant rate of 5% in the foreseeable future. Using the dividend growth (Gordon) model, what would you estimate its equity cost of capital to be? Show all the steps leading to your answer.

3. Two projects have the following NPV's and standard deviations:

Project A Project B

NPV 200 300

Standard deviation 75 100

a) Which of the two projects is more risky? Show all the steps leading to your answer.

b) Why?

4. What are the major ways that the risks of exchange rate changes can be hedged against?

5. What are the ways a multinational corporation can reposition its funds to increase its profits?

6. A function of government is to regulate "natural monopolies."

a) Explain what is a natural monopoly, and

b) Why it requires government regulation

#### Solution Preview

1. In game theory analysis, what is a "dominant strategy"?

A dominant strategy is one which always gives a player the best possible outcome, regardless of what the other player does. If strategy gives a player the highest payout for each of his opponent's moves, he will choose it, making it his dominant strategy.

2. A firm's most recent annual dividend was \$2 per share; its shares sell for \$40 in the stock market, and the company expects its dividend to grow at a constant rate of 5% in the foreseeable future. Using the dividend growth (Gordon) model, what would you estimate its equity cost of capital to be? Show all the steps leading to your answer.

The Gordon growth model gives us the formula: stock value = d/k-g, where

d = Expected dividend per share one year from now
k = Required rate of return for equity investor which is equal to the cost of equity for that company
g = Growth rate in dividends (in perpetuity)

So we have:
40 = 2 /k-5
Solving for k:
k -5 =2/40
k ...

\$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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