breaks down. To see this, consider once again the example of price competi-
tion played over a fixed number of periods. To find each firm’s optimal actions,
we work backward. In the last period, each firm’s dominant strategy is to cut
price, so this is what each does. (No threat of future price cuts can change this
because there is no tomorrow.) What about the next-to-last period? With prices
sure to be low in the last period, each firm’s best strategy is to cut price then as
well. In general, if low prices are expected in subsequent periods, each firm’s
best strategy is to cut prices one period earlier. Whatever the fixed number of
periods—3 or 300—this logic carries all the way back to period 1: The only
equilibrium is the repeated play of low prices.
Thus, we have something of a paradox. When the duration of price com-
petition is limited, super-rational players always will look ahead and see that a
price war is coming. Self-interest dictates that it is better to cut price earlier
than later. Both sides would prefer high prices, but rational players know that
high prices are not stable. Is there a way back to the cooperative, high-price
outcome? The answer is yes, if one admits the possibility of near-rationalplay.
Suppose there is a small chance that one or both sides will play cooperatively
because they fail to look ahead to the end of the game. (Perhaps they believe
the competition will go on indefinitely.) Injecting this “little bit” of irrational-
ity is a good thing. Now, even a perfectly rational player finds it in his or her self-
interest to charge a high price and maintain a cooperative equilibrium (at least
until near the end of the competition).^11426 Chapter 10 Game Theory and Competitive Strategy(^11) For an analysis of the repeated prisoner’s dilemma along these lines, see D. Kreps, P. Milgrom,
J. Roberts, and R. Wilson, “Rational Cooperation in the Finitely Repeated Prisoners’ Dilemma,”
Journal of Economic Theory(1982): 245–252. For an insightful discussion of reputation, see R. Wilson,
“Reputations in Games and Markets,” in A. Roth (Ed.), Game-Theoretic Models of Bargaining(New
York: Cambridge University Press, 1985).
The first step for each airline is to prepare estimates of its profits for alternative numbers
of departures it might schedule. We know that daily demand is 2,000 trips at a price of
$225 per trip. In other words, the airlines are competing for shares of a market having
$450,000 in total revenue. The cost for each additional daily departure is $20,000. Let’s
derive an expression for airline A’s profit. We denote the airlines’ numbers of departures
by a, b, and c, respectively. Then airline A’s profit (in thousands of dollars) can be
expressed as
Here A’s share of total revenue is a/(a b c). For instance, if all airlines fly identi-
cal numbers of flights, they obtain one-third market shares, or $150,000 in revenue
a 450
a
(abc)
20a.
A Battle for
Air Passengers
Revisited
c10GameTheoryandCompetitiveStrategy.qxd 9/29/11 1:33 PM Page 426