Page 628 - Microeconomics, Fourth Edition

c14gametheoryandstrategicbehavior.qxd 8/6/10 8:22 AM Page 602

602 CHAPTER 14 GAME THEORY AND STRATEGIC BEHAVIOR
Pipetran ABC’s profit is the left number in each cell; XYZ’s profit
No Expansion Small is the right number. For example, if ABC makes the
sweet cereal and XYZ produces the high-fiber cereal, an-
No Expansion 40, 18 28, 22 nual profits will be 50 million pesos for ABC and 60 mil-
Starline Small 48, 14 32, 16 lion pesos for XYZ.
Large 38, 10 24, 5
XYZ
High Fiber Sweet
a) If the two firms make their decisions about expansion 50, 60 30, 40
simultaneously, is there a unique Nash equilibrium? If so, ABC Sweet
what is it? If not, why not? Explain whether this game is High Fiber 20, 30 40, 60
an example of a prisoners’ dilemma.
b) Would Starline have a first-mover advantage if capac- a) If the two firms choose the type of plant simultane-
ities were chosen sequentially? If so, briefly explain how ously, is there a unique Nash equilibrium? If so, what is
it might credibly implement this strategy. it? If not, why not?
c) Suppose you were hired to advise Pipetran about its b) Would ABC have a first-mover advantage if capacities
choice of capacity. If Pipetran has the option of moving were chosen sequentially? If so, briefly explain how it
first, should it do so? Explain. might credibly implement this strategy.
c) Would XYZ have a first-mover advantage if capacities
14.23. ABC and XYZ are the two cereal manufacturers were chosen sequentially? If so, briefly explain how it
contemplating entry into a South American market. Each might credibly implement this strategy.
will be able to build one plant, and that plant can be used
to make either a cereal that is high in fiber and low in 14.24. Cities A, B, and C are located in different coun-
calories (High Fiber) or a less healthy cereal with a sweet tries. The only airline serving the market between A and
taste (Sweet). Once a plant is chosen to produce one kind B is Ajax Air. Its total cost is C Ajax 20Q AB . The airfare
of cereal, it will be prohibitively expensive to switch pro- between A and B is P AB . Also, the only carrier serving the
duction to the other type. The following table shows the market between B and C is Sky Air. Its total cost is C Sky
annual profit (in millions of pesos) that each firm would 20Q BC . The airfare between B and C is P BC . The two air-
earn given the production choices of the two firms. lines do not serve any other markets.

SKY

P BC P BC P BC P BC P BC P BC P BC P BC P BC
100 95 90 85 80 70 65 60 55
P AB 100 1600 2000 2800 3200 4000 4400 4800 5200
1600 1875 2275 2400 2500 2475 2400 2275

P AB 95 1875 2250 2625 3000 3375 4125 4500 4875 5250
2000 2250 2450 2600 2700 2750 2700 2600 2450
P AB 90 2100 2450 2800 3150 3500 4200 4550 4900 5250
2400 2625 2800 2925 3000 3000 2925 2800 2625

P AB 85 2275 2600 2925 3250 3575 4225 4550 4875 5200
2800 3000 3150 3250 3300 3250 3150 3000 2800
AJAX P AB 80 2400 2700 3000 3300 3600 4200 4500 4800 5100
3200 3375 3500 3575 3600 3500 3375 3200 2975
P AB 70 2500 2750 3000 3250 3500 4000 4250 4500 4750
4000 4125 4200 4225 4200 4000 3825 3600 3325
P AB 65 2475 2700 2925 3150 3375 3825 4050 4275 4500
4400 4500 4550 4550 4500 4250 4050 3800 3500

P AB 60 2400 2600 2800 3000 3200 3600 3800 4000 4200
4800 4875 4900 4875 4800 4500 4275 4000 3675
P AB 55 2275 2450 2625 2800 2975 3325 3500 3675 3850
5200 5250 5250 5200 5100 4750 4500 4200 3850