Chapter 10

1. In a one-shot game, if you advertise and your rival advertises, you will each earn $5

million in profits. If neither of you advertises, your rival will make $4million and you

will make $2million. If you advertise and your rival does not, you will make

$10million and your rival will make $3million. If your rival advertises and you do not,

you will make $1million and your rival will make $3million.

a. Write the above game in normal form.

b. Do you have a dominant strategy?

c. Does your rival have a dominant strategy?

d. What is the Nash equilibrium for the one-shot game? Explain.

2. 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 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.

2. Now suppose the game is infinitely repeated. If the discount rate is 10 percent, can you sustain cooperation? Explain

3. You are considering entering a market serviced by a monopolist. You currently earn $0 economic profits, while the monopolist earns $5. If you enter the market and the monopolist engages in a price war, you will lose $5 and the monopolist will earn $1. If the monopolist doesn’t engage in a price war, you will each earn profits of $2.

a. Write out the extensive form of the above game.

b. There are two Nash equilibria for the game. What are they? Explain.

3. Is there a subgame perfect equilibrium? Explain.

4. Based on your knowledge of one shot and repeated games, would you expect

tipping behavior to differ depending on whether a person is eating in a hometown

diner or in a restaurant located in Timbuktu? Explain.