Exchanges of Cost Information in the Airline Industry

Exchanges of Cost Information
in the Airline Industry.
Olivier Armantier¤ and Oliver Richardy
October 2000
)>IJH=?J
We empirically analyze exchanges of cost information in a multi-market
oligopoly model for the airline industry with entry and incomplete informa-
tion on marginal costs. We develop an algorithm to solve the Nash Equi-
librium numerically. We estimate the structural model of supply decisions
using data on the American Airlines and United Airlines duopoly at Chicago
O’Hare airport. Our results provide probabilities of entry, expected quanti-
ties, prices, and pro…ts on each market. Given the estimated parameters, we
simulate competition under a hypothetical agreement to exchange cost infor-
mation. We …nd that such exchanges would bene…t airlines without hurting
consumers.
Keywords: Structural Estimation, Incomplete Information, Airline Indus-
try, Exchanges of Cost Information, Entry, Network.
JEL Classi…cations : L11, D82, C15, C51, L93, R41
¤ Dept of Economics, SUNY Stony Brook NY, 11794. E-mail: olivier.armantier@sunysb.edu.
y Simon School of Business, University of Rochester, NY 14627; E-mail: richard@ssb.rochester.edu.
We thank Jean-Pierre Florens, John Hause, Philip Lederer, Glenn MacDonald, Soiliou Namoro, Jean-
Francois Richard, and Greg Sha¤er for very helpful discussions and suggestions. We also bene…ted from
comments received during seminars in Rochester, Toulouse and Stony Brook and from participants at
the Econometric Society World Congress (2000) and the International Conference on Game Theory
(2000) Oliver Richard thanks The Olin Foundation for …nancial assistance.

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1. Introduction
In the past ten years, the airline industry has witnessed a proliferation of marketing
alliances. Within alliances, airlines are able to market and sell tickets on their partner’s
‡ights and share revenues on joint ‡ights. These practices, known as code sharing, re-
quire exchanges of information on production processes, particularly on costs of produc-
tion. Given recent proposed alliances between major U.S. carriers, such as Continental
Airlines and Northwest Airlines, and American Airlines and US Airways, the implica-
tions of these cost information exchanges have become highly relevant. Armantier and
Richard (2000) …nd that, while exchanges of cost information raise expected pro…ts in
multi-market settings like the airline industry, expected consumer surplus may increase
or decrease depending upon the model’s parameters. Since policy makers and courts in
antitrust cases traditionally consider consumer surplus the deciding factor, this issue is
signi…cant. In this paper, we estimate the structural parameters of a multi-market model
of airline competition, and, to analyze how cost exchanges a¤ect consumer surplus, we
run some simulations.
In the airline literature, the existing empirical models by Reiss and Spiller (1989),
Berry (1992), Berry, Carnall, and Spiller (1996), Richard (2000) analyze decisions on
single-markets under complete information. We expand on the …ndings of the earlier lit-
erature as we recognize that …rms rarely observe their rivals’ costs accurately and entry
into a market typically a¤ects the state of other markets. Namely, to analyze exchanges
of cost information, we propose a static oligopoly model with incomplete information
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on costs and simultaneous entry decisions across multiple markets with demand com-
plementarities. There are no …xed costs and marginal costs are assumed to be random
private signals, known to the …rm but not its rivals. These are drawn from a joint distri-
bution, which is common knowledge among …rms. Our model is analytically intractable,
and we propose an algorithm, based upon Monte-Carlo simulations, to determine the
Bayesian Nash Equilibrium numerically.
We apply this model to American Airlines (AA) and United Airlines’ (UA) duopoly
competition at Chicago O’Hare airport. The sample data, from the third quarter of
1993, includes 83 markets with ‡ights from at least one of AA or UA, and 17 major
markets with no ‡ights. First, we estimate the demand functions, which we assume to
be exogenous to the structural model. We then estimate the distribution of marginal
costs with the structural inference method recently proposed by Florens, Protopopescu,
and Richard (1999) for games of incomplete information. We …nd an average cost per
passenger/mile of $0.165. This …gure is consistent with trade publications. Our method
also provides probabilities of entry, expected quantities of passengers, prices, and pro…ts.
The results closely match observed values.
Finally, we assume that AA and UA agree to exchange cost information truthfully.
In this scenario, the two airlines compete under complete information. Using the esti-
mated distribution of marginal costs, we simulate and compare the airlines’ equilibrium
decisions under both incomplete and complete information. As expected, the average
pro…ts increase on every market when AA and UA exchange cost information. Interest-
ingly, these exchanges leave the expected consumer surplus essentially unchanged, and
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consumers typically bene…t on a majority of markets (57%). Hence, a marketing alliance
between AA and UA to exchange cost information would be advantageous to airlines
without hurting consumers.
The paper is structured as follows. We introduce the theoretic model in Section 2.
We propose an algorithm to solve the Bayesian Nash Equilibrium in Section 3. Section
4 discusses the application to the airline industry. In Section 5, we discuss the structural
estimation method and present our …ndings. Section 6 then analyzes exchanges of cost
information. Section 7 concludes.
2. A Model of Firms’ Decisions
To analyze exchanges of cost information, we develop the following theoretic model.
There are N symmetric …rms (i = 1; ::; N) and M markets (m = 1; :::; M). Firms
decide simultaneously whether to enter and how much to produce on each of the M
markets.
There are no …xed costs, and marginal costs of production are constant. We assume
incomplete information on marginal costs. Each …rm i is endowed with a vector of
private types ci = (ci;1; :::; ci;m; :::; ci;M) where ci;m is …rm i’s constant marginal cost of
production on market m. Firms know their own marginal costs, but they do not observe
their rivals’ c¡i = (c1; ::; ci¡1; ci+1;; ::; cN) when deciding upon an optimal strategy: Cost
values ci;m are independently and identically distributed (hereafter i.i.d.) across …rms
and independently distributed across markets. Let fm (:jµ) denote the probability density
4

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function (p.d.f.) of ci;m indexed by the vector µ 2 <k: The p.d.f. fm (:) and the parameter
µ are common knowledge among …rms.
The demand function on a market is common knowledge and exogenously deter-
mined. It is linear and symmetric across …rms. If production is limited to one market,
then goods on that market are perceived to be perfect substitutes across …rms. Goods
across markets are complements and expressed in a common unit. The price for a rep-
resentative customer of …rm i on market m, Pi;m, is a non-negative function of quantity
choices across all M markets:
M
X
M
X N
X
N
X
Pi;m = ®m + ¯m
qi;m + ¸m
qj;m ¡ °m
qj;m
(2.1)
m6=m
m6=m j6=i
j=1
where qi;m is …rm i’s quantity on market m and ®m; ¯m; ¸m; °m are parameters verifying
®m > 0; °m > ¯m ¸ ¸m > 0: This speci…cation allows for the level of complementarity
to di¤er across …rms (i.e., ¯m ¸ ¸m). Namely, a consumer who purchases a good may
be more willing to buy another good from the same …rm than from another …rm. Brand
loyalty or compatibility problems across brands may explain this behavior.1 Hence, con-
sumers’ willingness to pay for goods which would be considered perfect substitutes if
there were no complementarities may vary. We also assume that …rm i0s price on a
market m is equally a¤ected by an increase in quantity on any market m0 6= m, even
when m0 is a new market.2 We can interpret ¯m and ¸m as the marginal increase in a
consumer’s willingness to pay for good m due to one more unit supplied on a market
m0 6= m.
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Given their marginal costs, …rms simultaneously decide whether to enter and how
much to produce on each of the M markets. In other words, given ci; …rm i maximizes
its expected pro…ts across all M markets by selecting non-negative quantities q¤i =
³
´
q¤i;1; ::; q¤i;m such that
M
:
q¤i = 'i (ci; µ) = Arg max
E [(Pi;m ¡ ci;m) qi;mj µ; ci]
fqi;mgm=1;::;M m=1
subject to
qi;m ¸ 0
8m = 1; :::; M
(2.2)
where 'i (ci; µ) is …rm i0s equilibrium strategy function. We do not impose that pro…ts
nor expected pro…ts are positive on a given market. In the subsequent simulations, …rms
have positive expected pro…ts on every market even if they sometimes incur losses. Note
as well that the non-negativity constraints on prices are non-binding in the simulations.
Substituting (2.1) into (2.2), we have that
M
:
M
:
M
: N
:
q¤i = Arg max
(®m + ¯m
qi;m + ¸m
E [qj;mjµ; ci]
fqi;mgm=1;:::M m=1
m6=m
m6=m j6=i
N
:
¡°m
E [qj;mjµ; ci] ¡ °mqi;m ¡ ci;m) qi;m
(2.3)
j6=i
subject to
qi;m ¸ 0
8m = 1; :::; M
Subsequent to their quantity choices, …rms observe the realizations of prices and pro…ts
on each of the M markets.
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3. Computing the Bayesian Nash Equilibrium Solution
To analyze exchanges of cost information, we need to derive the Bayesian Nash equi-
librium. We …nd that there is no analytical solution to the problem, and we propose
an algorithm, based upon Monte-Carlo simulations of the game, to …nd the equilibrium
solution numerically. This numerical technique is central to our analysis. We use it
both to estimate the structural model and to quantify the e¤ects of cost information
exchanges on consumer surplus.
3.1. The Kuhn-Tucker conditions
The Kuhn-Tucker conditions for the constrained optimization problem in (2.3) are as
follows:
M
:
M
: N
:
Vi;m = ®m +
(¯m + ¯m) qi;m + ¸m
E [qj;mjµ; ci]
m6=m
m6=m j6=i
N
:
¡°m
E [qj;mjµ; ci] ¡ 2°mqi;m ¡ ci;m · 0
j6=i
qi;mVi;m = 0
and
qi;m ¸ 0
8m = 1; :::; M
8i = 1; :::; N
(3.1)
where Vi;m is the partial derivative of (2.3) with respect to qi;m.3
Since …rms are ex-ante symmetric and private signals are i.i.d. across …rms, we …nd
that at the equilibrium E [qj;mjµ; ci] = E [qj;mjµ; ci] = E [qmjµ] 8j 6= i 8i 6= i0 or 8j 6=
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j0: We then write
M
:
M
:
Vi;m = ®m+
(¯m + ¯m) qi;m+¸0m
E [qmjµ]¡°0mE [qmjµ]¡2°mqi;m¡ci;m (3.2)
m6=m
m6=m
where ¸0m = ¸m(N ¡ 1) and °0m = °m(N ¡1): The Kuhn-Tucker conditions are invariant
to a permutation of player indices and equilibrium strategies are symmetric across …rms
'i (:; µ) = 'j (:; µ) = ' (:; µ) 8j 6= i: We thus focus on the decisions of a representative
…rm i. The Kuhn-Tucker conditions imply that
qi;m > 0 () ci;m < ci;m (ci;¡m)
8 m = 1; :::M
where
M
:
M
:
ci;m (ci;¡m) = ®m +
(¯m + ¯m) qi;m + ¸0m
E [qmjµ] ¡ °0mE [qmjµ] (3.3)
m6=m
m6=m
with ci;¡m = (ci;1; ::; ci;m¡1; ci;m+1;; ::; ci;M): Firm i only enters into market m if its mar-
ginal cost ci;m is below ci;m (ci;¡m). Note that the threshold value ci;m (ci;¡m) is a function
of …rm i0s marginal costs on every market m0 6= m: Given that the model’s demand and
cost functions are linear in quantities, the value ci;m (ci;¡m) is uniquely de…ned on each
market m:
Inserting equation (3.3) into equation (3.2), we …nd that the solution to the opti-
mization problem (2.3) veri…es the following:
Ã
!
c
q
i;m (ci;¡m) ¡ ci;m
i;m =
I
2°
fci;m·ci;mci;¡mg
8m = 1; :::M
(3.4)
m
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where I
is the indicator function de…ned as
fci;m·ci;m(ci;¡m)g
(
)
1
when x · 0
Ifx·g =
:
0
otherwise
Now, inserting equation (3.4) into equation (3.3) leads to
M
Ã
!
X
(c
0 = ®
i;m0 (ci;¡m0 ) ¡ ci;m0)
³
´o
m +
(¯m + ¯m0)
In
2°
c
c
m06=m
m0
i;m0 ·ci;m0
i;¡m0
M
X
+¸0m
E [qm0jµ] ¡ °0mE [qmjµ] ¡ ci;m (ci;¡m)
8m = 1; :::M
(3.5)
m06=m
To determine equilibrium quantities, we need to solve the system of equations (3.5)
and then (3.4). Note that (3.5) depends upon E [qjµ] = (E [q1jµ] ; :::; E [qMjµ]) : In this
case, unlike a complete information setting, …rms cannot predict the exact quantities
that their rivals produce at the Nash solution. To determine their best strategies, …rms
can rely only upon their rivals’ expected quantities, E [qjµ]. There is no analytically
tractable way, however, to calculate E [qjµ] :
3.2. A Numerical solution
To determine the Nash Equilibrium, we propose to replace E [qjµ] by an approximation
>
E [qjµ] : Intuitively, >
E [qjµ] is the …xed point solution of a problem matching a poten-
tial expected quantity to its empirical counterpart as calculated across Monte Carlo
simulations.
For a given µ; we simulate S vectors of private types4 (using the Common Random
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Number technique) for the representative …rm i; fAci;sgs=1;:::;S with Aci;s = (Aci;s;1; :::; Aci;s;M) :
The approximation >
E [qjµ] is then the solution of
min jj" ¡ q
"
i (") jj
(3.6)
where " = ("
2S
1; :::; "M ) is a potential value for E [qjµ]; qi (") = 1S
s=1 A
qi;s (Aci;s; ") is the
empirical mean of simulated quantities; and Aqi;s (Aci;s; ") is the numerical solution of the
system of equations (3.5) and (3.4) given E [qjµ] = " and ci = Aci;s:
In practice, (3.6) is solved numerically with the simplex method. >
E [qjµ] = " is a
reasonable approximation of the expected quantity E [qjµ] when " becomes arbitrarily
close to its simulated empirical counterpart qi ("). The calculation of >
E [qjµ] is time-
consuming, but it is not computationally challenging. The equations to be solved nu-
merically are linear up to an indicator function, and there exist numerous numerical
procedures that solve these systems in a matter of seconds.
Once >
E [qjµ] has been determined, we can calculate from (3.5) and (3.4) the equi-
librium quantities for a given cost vector ci: Symmetrically, we can invert the strategy
function and calculate fci;m (qi) ; ci;m (qi;¡m)gm=1;:::M for a vector of observed equilibrium
quantities qi from (3.3) and (3.4): The econometric technique used in the application to
the airline industry requires an inversion of the equilibrium strategy (see Section 5).
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