# 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?

https://brainmass.com/economics/game-theory/nash-equilibrium-game-theory-57345

#### 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.