Page 627 - Microeconomics, Fourth Edition

c14gametheoryandstrategicbehavior.qxd 8/6/10 8:22 AM Page 601

PROBLEMS 601
c) Suppose that aircraft orders are received once a year that if the buyer purchases the product and learns that he
rather than once a quarter. That is, Boeing and Airbus has bought a high-quality good, he will return the next
will compete with each other for an order this year (with month and buy again. Indeed, he will continue to pur-
payoffs given in the table above), but their next compet- chase, month after month (potentially forever!), as long
itive encounter will not occur for another year. In terms as the quality of the product he purchased in the previous
of evaluating present and future payoffs, suppose that month is high. However, if the buyer is ever unpleasantly
each firm views a stream of payoffs of $1 starting next surprised—that is, if the seller sells him a low-quality
year and received every year thereafter as equivalent to good in a particular month—he will refuse to purchase
$10 received immediately this year. Again assuming that from the seller forever after. Suppose that the seller
Airbus will follow the policy in its public statement knows that the buyer is going to behave in this fashion.
above, what price would you recommend that Boeing Further, let’s imagine that the seller evaluates profits in
charge in this year and beyond? the following way: a stream of payoffs of $1 starting next
month and received in every month thereafter has exactly
14.20. Consider a buyer who, in the upcoming month, the same value as a one-time payoff of $50 received im-
will make a decision about whether to purchase a good mediately this month. Will the seller offer a low-quality
from a monopoly seller. The seller “advertises” that it of- good or a high-quality good?
fers a high-quality product (and the price that it has set is
based on that claim). However, by substituting low-quality 14.21. Two firms are competing in an oligopolistic
components for higher-quality ones, the seller can re- industry. Firm 1, the larger of the two firms, is contemplat-
duce the quality of the product it sells to the buyer, and ing its capacity strategy, which could be either “aggressive”
in so doing, the seller can lower the variable and fixed or “passive.” The aggressive strategy involves a large
costs of making the product. The product quality is not increase in capacity aimed at increasing the firm’s market
observable to the buyer at the time of purchase, and so the share, while the passive strategy involves no change in the
buyer cannot tell, at that point, whether he is getting a firm’s capacity. Firm 2, the smaller competitor, is also
high-quality or a low-quality good. Only after he begins pondering its capacity expansion strategy; it will also
to use the product does the buyer learn the quality of the choose between an aggressive strategy and a passive strat-
good he has purchased. egy. The following table shows the profits associated with
The payoffs that accrue to the buyer and seller from each pair of choices:
this encounter are as follows:

Seller Firm 2
Aggressive Passive
Sell High-Quality Sell Low-Quality
Product Product Aggressive 25, 9 33, 10
Firm 1
Purchase $5, $6 $4, $12 Passive 30, 13 36, 12
Buyer
Do Not $0, $4 $0, $1
Purchase a) If both firms decide their strategies simultaneously,
what is the Nash equilibrium?
The buyer’s payoff (consumer surplus) is listed first; the
seller’s payoff (profit) is listed second. b) If Firm 1 could move first and credibly commit to its
Answer each of the following questions, using the capacity expansion strategy, what is its optimal strategy?
preceding table. What will Firm 2 do?
a) What are the Nash equilibrium strategies for the buyer 14.22. The only two firms moving crude oil from an
and seller in this game under the assumption that it is oil-producing region to a port in Atlantis are pipelines:
played just once? Starline and Pipetran. The following table shows the an-
b) Let’s again suppose that the game is played just once nual profit (in millions of euros) that each firm would
(i.e., the buyer makes at most one purchase). But suppose earn at different capacities. Starline’s profit is the left
that before the game is played, the seller can commit to of- number in each cell; Pipetran’s profit is the right number.
fering a warranty that gives the buyer a monetary payment At the current capacities (with no expansion) Starline is
W in the event that he buys the product and is unhappy earning 40 million euros, and Pipetran is earning 18 mil-
with the product he purchases. What is the smallest value lion euros annually. Each company is considering an
of W such that the seller chooses to offer a high-quality expansion of its capacity. Since Pipetran is a fairly small
product and the buyer chooses to purchase? company, it can consider only a small expansion to its
c) Instead of the warranty, let’s now allow for the possibil- capacity. Starline has the ability to consider both a small
ity of repeat purchases by the buyer. In particular, suppose and a large expansion.