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EC 515 Game Theory Problems.

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 advertise, your rival will make $4 million and you will make $2 million. If you advertise and your rival does not, you will make $10 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.

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?

e.How much would you be willing to bribe your rival not to advertise?

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 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.Write out the normal form of the above game.

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

3.   OPEC was an effective cartel for many years, but recently it has sometimes been unable to maintain a high price of oil. What factors do you think are contributing to the demise of OPEC?

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.

5.According to a spokesperson for cereal maker Kellogg, “… for the past several years, our individual company growth has come out of the other fellow’s hide.”[1]

a.What implications does this statement have for the level of advertising in the cereal industry?



Firm B
Firm A
Strategy
Advertise
Don’t Advertise
Advertise
4, 4
20, 1
Don’t advertise
1, 20
10, 10

6.You are the manager of the ABC novelty store, and your only competitor is the XYZ novelty store. You are both trying to decide on which magic tricks and party favors to carry in stock. The product mixes available to both of you are low, medium, and high in variety. Your expected earnings in this market are shown in the following table.

 



Firm XYZ

Firm ABC
Strategy
Low 
Medium
High
 
Low
100,100
150, 200
200, 300
 
Medium
200, 75
125, 150
225, 195 
 
High
300, 200
100, 225
150, 250
 







a.Find the Nash equilibrium (or equilibria) for a simultaneous-move, one-shot play of this game.

b.What outcome would you expect in this one-shot game? Why?

7.You are the owner-operator of the Better Gas Station in a small southeastern town. Over the past 20 years, you and your rival have successfully kept prices at a very high level. You recently learned that your competitor is retiring and closing his station in two weeks. What should you do today? Why?

8.According to various trade publications, over 200,000 changes are made in airfares each day. Why do you think this is the case?

9.Two executives were arrested by authorities for embezzling money from their firm. Short of a confession, the prosecutor only had enough evidence to put them away for 10 years. Given a confession, however, she was certain to put them behind bars for life without parole, since they killed a law enforcement officer who was investigating the case. The prosecutor put the two prisoners in separate rooms, and told them the following: “If you confess and your partner does not, I’ll give you a year’s probated sentence but put your partner in the slammer for life without parole. Of course, if your partner confesses and you don’t, you’ll get the life sentence without parole and he’ll get one year’s probation. I must warn you, however, that if you both confess I’ll have enough evidence to put you both away for life without parole.”

a.Do you think the prosecutor’s bargain will induce the two executives to confess? Explain.

b.Would your answer change if the life sentence carried the possibility of parole? Explain.

10.In the early 1990s, there was considerable uncertainty in the computer industry about whether the dominant operating system for future personal computers would be IBM’s OS/2 or Microsoft’s Windows. Ultimately, Windows emerged as the dominant system despite the fact that several trade publications viewed OS/2 as the superior system. Why do you think this outcome prevailed?

11.Suppose Philips and Toshiba are the first companies to introduce digital versatile disk (DVD) machines to the market. Studies by the firms suggest that consumers who purchase consumer electronics are very brand-loyal. To capture future loyalties, each firm will attempt to maximize its initial market share, for one time only, by setting prices. An economist has estimated the initial market share of each firm under different pricing scenarios. Her results are captured in the following payoff matrix.

 


Toshiba
Philips
Strategy
P = $250
P = $500
P = $1,000
P = $250
60%, 40%
75%, 25%
95%, 5%
P = $500
25%, 75%
90%, 10%
75%, 25%
P = $1,000
5%, 95%
25%, 75%
70%, 30%

a.Given this scenario, if you were in charge of pricing at Philips, what price would you charge? Explain.

b.What market share would you anticipate as a result of your pricing strategy? Explain.


Review questions to know on final:

12.  Draw, label and explain a perfectly competitive firm making an economic loss but not shutting down in the short run.
13.  Draw and label a monopoly firm making an economic profit.  
14.  Draw, label and define the 10 production and cost curves we discussed in class.
15.  Explain the items that will impact demand.
16.  Explain the items that will impact supply.
17. Discuss price elasticity of demand (what is it and what will impact it)