Question content area

Part $1$

You and a competitor own two stores in the same town that sell musical instruments. The two of you can either set high prices or set low prices. You know your profits but can only estimate your$$ rival's profits. If you both set high$$ prices, your economic profit will be

$$$$44$

$$million$,$ and you think your rival will make a large profit. If you both set low$$ prices, your economic profit will be$$ zero, and you think your rival also will make no economic profit. If you set high prices and your rival sets low$$ prices, you will have an economic loss of

$$$$22$

$$million$,$ and you forecast that your rival will have a very large profit.$$ Finally, if you set low prices and your rival sets high$$ prices, you will have a profit of

$$$$55$

$$million$,$ and you believe your rival will have an economic loss.

Part $2$

Complete the payoff matrix for this game.

$($Enter

a negative sign if your answer is a

loss.$)$

Rival$($R$)$

Set High Prices

Set Low Prices

You$($Y$)$

Set High

Prices

$$Y:

$$$enter your response here

million

$$Y:

$$$enter your response here

million

$$R:

$$

$$

Large

Zero

Same as you

Very large

Loss

R$$:

$$

$$

Zero

Same as you

Very large

Large

Loss

Set Low Prices

Y$$:

$$$enter your response here

million

Y$$:

$$$enter your response here

million

R$$:

$$

$$

Loss

Large

Very large

Same as you

Zero

R$$:

$$

$$

Large

Loss

Zero

Very large

Part $3$

If the game is played only$$ once, do you have a dominant$$ strategy? If$$ so$,$ what is$$ it$?$ Does your rival have a dominant$$ strategy? If$$ so$,$ what is$$ it$?$ What is the Nash equilibrium of the$$ game?

A$.$

Your dominant strategy is to set low prices. Your$$ rival's dominant strategy is to set low$$ prices, too. In the Nash$$ equilibrium, both you and your rival set low prices.

B$.$

Your dominant strategy is to set high prices. Your$$ rival's dominant strategy is to set low prices. In the Nash$$ equilibrium, both you and your rival set low prices.

C$.$

You do not have a dominant strategy. Your$$ rival's dominant strategy is to set low prices. In the Nash$$ equilibrium, both you and your rival set low prices.

D$.$

Your dominant strategy is to set high prices. Your rival does not have a dominant strategy. In the Nash$$ equilibrium, both you and your rival set high prices.

Part $4$

If the game is played$$ repeatedly, what is the cooperative$$ equilibrium? What strategy$($or strategies$)$ could you$$ adopt?

A$.$

In the cooperative$$ equilibrium, you and your rival both set low prices. You could adopt a mixed strategy to give your rival an incentive to cooperate.

B$.$

In the cooperative$$ equilibrium, you and your rival both set high prices. You could adopt a trigger strategy to give your rival an incentive to cooperate.

C$.$

In the cooperative$$ equilibrium, you and your rival both set low prices. You could adopt a trigger strategy to give your rival an incentive to cooperate.

D$.$

In the cooperative$$ equilibrium, you and your rival both set high prices. You could adopt a mixed strategy to give your rival an incentive to cooperate.