# Nash equilibrium

You operate in a duopoly in which you and a rival must simultaneously decide what price to advertise in the weekly newspaper. If you each charge a low price, you each earn zero profits. If you each charge a high price, you each earn profits of $3. If you charge different prices, the one charging the higher price loses $5 and the one charging the lower price makes $5.

a. Find the Nash equilibrium for a one-shot version of this game.

b. Now suppose the game is infinitely repeated. If the interest rate is 10 percent, can you do better than you could in a one-shot play of the game? Explain.

c. Explain how "history" affects the ability of firms in this game to achieve an outcome superior to that of the one-shot version of the game.

https://brainmass.com/economics/game-theory/nash-equilibrium-20544

#### Solution Preview

Nash Equilibrium

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<br>a. Normal Form of the game

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<br>(Columns of the table may get mis-aligned because of BM formatting my output somewhat incorrectly; my apologies, please)

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<br> Your Rival

<br> Low Price High Price

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<br> Low (0,0) (5,-5)

<br> You

<br> High (-5,5) (3,3) ...

#### Solution Summary

Find the Nash equilibrium for a one-shot version of this game.