Competitive Strategy 427each. If airline A provides half the total flights, it claims half the total revenue, and
so on. The second term in the profit expression is the total cost of providing this num-
ber of departures. (Analogous expressions apply for the other airlines.) Inspection of
this equation reveals the airline’s basic trade-off: By flying more flights, it claims a
greater share of revenue, at the same time incurring additional costs. Moreover, the
larger the number of competitors’ flights, the smaller the airline’s revenue share. If all
airlines fly “too many” flights, they all incur large costs, but the result remains a rev-
enue standoff.
Table 10.7 lists the typical airline’s payoff table. Note two things about the table. First,
it has condensed the decisions of the other two airlines into one variable: the total num-
ber of competitor flights. (The columns list numbers of these flights ranging from 5 to
17.) From the profit equation, we observe that an airline’s profit depends only on the
number of its own flights (a) and the total number of competitor flights (b c). For
example, if airline A mounts five flights and B and C have a total of five flights, A’s profit
is (5/10)(450) (5)(20) $125 thousand, as shown in Table 10.7. Second, only the air-
line’s own profit is listed (to save space). As we would expect, each firm’s profit is highly
sensitive to the number of flights flown by its competitors. By reading across the payoffs
in any row, we see that an airline’s profit falls drastically as the number of competing
flights increases.
If the three airlines are going to compete month after month, how might they set
their number of departures each period? In answering this question, we consider two pos-
sible benchmarks: equilibrium behavior and collusive behavior.
To help identify equilibrium behavior, best-response payoffs are highlighted in Table
10.7. For example, if its competitors schedule only 5 total flights, the airline’s best
response is 6 flights, earning it $125,500 (the highest payoff in column 1); against 13
flights, the airline’s best response is 4 flights; and so on. The table shows that no airline
has a dominant strategy. (The more numerous the competitors’ flights, the fewer flights
the airline should fly.) However, it is striking that the best responses congregate closely
around five flights (ranging from three to six). In fact, the unique equilibrium has eachTABLE 10.7
An Airline’s Payoff
TableThe airline’s best
responses are high-
lighted. In equilibrium,
each of the three air-
lines flies five daily
departures.Total Number of Competitors’ Flights
5 6 7 8 9 101112131415 16 17
2 50.0 50.0 50.0 50.0 41.8 35.0 29.2 24.3 20.0 16.3 12.9 10.0 7.4
Own 3 75.0 75.0 75.0 62.7 52.5 43.8 36.4 30.0 24.4 19.4 15.0 11.1 7.5
Number 4 100.0 100.0 83.6 70.0 58.5 48.6 40.0 32.5 25.9 20.0 14.7 10.0 5.7
of Flights 5 125.0 104.5 87.5 73.1 60.7 50.0 40.6 32.4 25.0 18.4 12.5 7.1 2.3
6 125.5 105.0 87.7 72.9 60.0 48.8 38.8 30.0 22.1 15.0 8.6 2.7 2.6
7 122.5 102.3 85.0 70.0 56.9 45.3 35.0 25.8 17.5 10.0 3.2 3.0 8.8
8 116.9 97.1 80.0 65.0 51.8 40.0 29.5 20.0 11.4 3.63.510.016.0c10GameTheoryandCompetitiveStrategy.qxd 9/29/11 1:33 PM Page 427