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c14gametheoryandstrategicbehavior.qxd 8/6/10 8:22 AM Page 598

598 CHAPTER 14 GAME THEORY AND STRATEGIC BEHAVIOR
a) Does either player have a dominant strategy? Explain. Nokia
b) Is there a Nash equilibrium in this game? If so what is it? Enter Do Not Enter
c) Is this game an example of the prisoners’ dilemma? Enter 1,000, 1,000 500, 0
Explain. Alcatel Do Not Enter 0, 500 0, 0
14.6. Asahi and Kirin are the two largest sellers of beer
in Japan. These two firms compete head to head in the Ignoring mixed strategies, find all of the Nash equilibria
dry beer category in Japan. The following table shows in this game.
the profit (in millions of yen) that each firm earns when
it charges different prices for its beer: 14.9. ABC and XYZ are the only two firms selling giz-
mos in Europe. The following table shows the profit (in
Kirin millions of euros) that each firm earns at different prices
¥630 ¥660 ¥690 ¥720 (in euros per unit). ABC’s profit is the left number in each
cell; XYZ’s profit is the right number.
¥630 180, 180 184, 178 185, 175 186, 173
¥660 178, 184 183, 183 192, 182 194, 180 XYZ
Asahi Price 20 24 28 32
¥690 175, 185 182, 192 191, 191 198, 190
¥720 173, 186 180, 194 190, 198 196, 196 20 60, 60 68, 56 70, 50 72, 46
24 56, 68 66, 66 84, 84 88, 60
ABC
a) Does Asahi have a dominant strategy? Does Kirin? 28 50, 70 64, 84 82, 82 96, 80
b) Both Asahi and Kirin have a dominated strategy: Find 32 46, 72 60, 88 80, 96 92, 92
and identify it.
c) Assume that Asahi and Kirin will not play the domi- Is there a unique Nash equilibrium in this game? If so,
nated strategy you identified in part (b) (i.e., cross out the what is it? If not, why not? Explain clearly how you ar-
dominated strategy for each firm in the table). Having rive at your answer.
eliminated the dominated strategy, show that Asahi and
Kirin now have another dominated strategy. 14.10. Two pipeline firms are contemplating entry into
a market delivering crude oil from a port to a refinery.
d) Assume that Asahi and Kirin will not play the domi- Pipeline 1, the larger of the two firms, is contemplating
nated strategy you identified in part (c). Having elimi- its capacity strategy, which we might broadly character-
nated this dominated strategy, determine whether Asahi ize as “aggressive” and “passive.” The “aggressive” strat-
and Kirin now have a dominant strategy.
egy involves a large increase in capacity aimed at increas-
e) What is the Nash equilibrium in this game? ing the firm’s market share, while the passive strategy
14.7. Consider the following game: involves no change in the firm’s capacity. Pipeline 2, the
smaller competitor, is also pondering its capacity expan-
Player 2 sion strategy; it will also choose between an “aggressive
Left Right strategy” or a “passive strategy.” The following table
shows the present value of the profits associated with
Up 1, 4 100, 3
Player 1 each pair of choices made by the two firms:
Down 0, 3 0, 2
Pipeline 2
Aggressive Passive
a) What is the Nash equilibrium in this game?
Aggressive 75, 25 100, 30
b) If you were Player 1, how would you play this game? Pipeline 1
Passive 90, 45 110, 40
14.8. It is the year 2099, and the moon has been colo-
nized by humans. Alcatel (the French telecom equipment a) If both firms decide their strategies simultaneously,
company) and Nokia (the Finnish telecom equipment what is the Nash equilibrium?
company) are trying to decide whether to invest in the b) If Pipeline 1 could move first and credibly commit to
first cellular telecommunications system on the moon. its capacity expansion strategy, what is its optimal strat-
The market is big enough to support just one firm prof- egy? What will Pipeline 2 do?
itably. Both companies must make huge expenditures in
order to construct a cellular network on the moon. The 14.11. Lucy and Ricky are making plans for Saturday
payoffs that each firm gets when it enters or does not night. They can go to either a ballet or a boxing match.
enter the moon market are as follows: Each will make the choice independently, although as