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    Nash equilibrium and Game Theory

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    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?

    © BrainMass Inc. brainmass.com October 9, 2019, 5:26 pm ad1c9bdddf
    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.

    $2.19