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# Nash equilibrium and Game Theory

In a one-shot game, if you advertise and your rival advertises, you will earn \$7 million and your rival will earn \$2 million in profits. If neither of you advertise, your rival will make \$4 million and you will make \$2 million. If you advertise and your rival does not, you will make \$8 million and your rival will make \$3 million. If your rival advertises and you do not, you will make \$1 million and your rival will make \$3 million.

Here are my questions:
- What is the above game in normal form?
- Is there a dominant strategy? If yes, what is it?
- Does the rival have a dominant strategy? If yes, what is it?
- What is the Nash equilibrium for the one-shot game?

#### Solution Preview

Hello!
Here's the above game in normal form:

Rival Advertises Rival Doesn't Adv

You Advertise (7,2) (8,3)

You Don't Adv (1,3) (2,4)

[the numbers in the left represent your profits, the ones in the right represent your rival's]

Let's see if there's a dominant startegy for you. A dominant strategy is a choice that maximizes profits no matter what the other player does. So let's check what you should do for each of the choices your rival could make:

- If your Rival ...

#### Solution Summary

Nash equilibrium is considered.

\$2.19