8/6/2019 Economics of Revenue Mgt Pricing Competition and Seat Allocation
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Economics of Revenue Management:
Pricing, Competition, and Seat Allocation.
Serguei Netessine*
The Wharton School,
University of Pennsylvania
Robert Shumsky
W. E. Simon Graduate School of Business Administration
University of Rochester
Email: [email protected]
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2
American
United
6:37
172 seats
6:05
108 seats
7:25
155 seats
21-day advance purchase round-trip: $289
14-day advance purchase round-trip: $318
7-day advance purchase round-trip: $798
Unrestricted full fare: $664 each way
10:00
128 seats
13:13
108 seats
16:35
108 seats
9:39172 seats
13:14
109 seats16:53
172 seats
20:03
109 seats
Same for both
airlines
Rochester to Chicago Timetable, December, 2000
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3
“Horizontal” competition in US airline industry
From S. A. Morrison. 1998. “Airline Service: The evolution of competition since deregulation.”
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The Full Revenue Management Game
ChooseB1,B2
Accept low
fare passengers
Accept overflow high
fare passengers
Accept high
fare passengers
Accept overflow
low fare passengers
Additional Assumptions
• Two noncooperative airlines, each with capacity C.
• Identical prices.
• Two passenger classes, H (High) and L (Low) fares.
• All passengers who cannot find a seat on one airline ‘overflow’ tothe other airline.
• The following order of events:
D L
realized
D H
realized
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The Full Game
Low fare
class
High fare
class D H1
D L1
Low fareclass
High fare
class D H2
D L2
Airline 1 Airline 2
(D L1 - B1 )+
(D L2 - B2 )+
B1
B2
Min(B1 ,D L1 )
Min(B2 ,D L2 )
(D H1 - R1 )+
(D H2 - R2 )+
+−+= )( j Lj Li
T
Li B D D D = total low-fare demand
= space available for high-fare),min( i
T
Lii B DC R −=
= total high-fare demand+−+= )( j Hj Hi
T
Hi R D D D
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The Full Game
Airline 1’s objective:
),min(),min(),( 1111211 R D p B D p E B BT
H H
T
L L +=π
First-order conditions
0),,,Pr(
),Pr()Pr(
11222211
111111
=−<><>−
>−>−>
BC D R D B D B D p
B D BC D p B D p
T
H H
T
L L H
T LT H H T L L
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Two Airline Response Functions and Nash Equilibria
0 50 100 150 200 0
50
100
150
200
B1
B2
r 1(B2)
r 2(B1)
0 10 20 30 40 50 0
10
20
30
40
50
B1
B2 r 1(B2)
r 2(B1)
For both examples, correlation( D L, D H ) = 0
E( D L) > E( D H ) E( D L) << E( D H )
With C = 200.
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Example: No Pure-Strategy Equilibrium
0 50 100 150 200 0
50
100
150
200
B1
B2
r 1(B2)
r 2(B1)
correlation( D L, D H ) = -0.9
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‘Partial Games’
• High-fare overflow only (no low-fare overflow)èA good approximation if low fare demand is high
èA pure strategy equilibrium must exist.
è Under certain assumptions, equilibrium is unique.
• Low-fare overflow is delayed until the ‘end’ of the
game.èA pure strategy equilibrium must exist.
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Competition vs. Monopoly
• A monopoly maximizes the sum of the profits of both flights (#
available seats = 2C)
• What can we say about total booking limit?
correlation( D L
, D H
)
T o t a l b
o o k i n g l i m i t ( B 1 +
B 2
)
monopoly
competition
-0.2 0 0.2 0.4 0.6 0.8250
260
270
280
290
300
310
320
330
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Impact on Service Level
service level = proportion of passengers served
by either flight
-0.2 0 0.2 0.4 0.6 0.80.4
0.5
0.6
0.7
0.8
0.9
correlation( D L, D H )
S e r v i c e L e v e l
monopoly
competition
monopoly
competition
High-fare
service level
Low-fare
service level
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Insights
• Instability of full game
• Pure-strategy equilibrium in partial games
• One partial game (high-fare overflow only) is
sometimes a good approximation to the full game.
• Lower booking limits under competition
(analytically confirmed for a partial game).• Impact on customer service.
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Fixed prices assumption
From S. A. Morrison and C. Winston. 1995. “The evolution of the airline industry.”
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Evolution of prices
From S. A. Morrison. 1998. “The evolution of competition since deregulation.”
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Economic model
Limited fixed number of seats C, two fares: high and low
L
L
b
a
2 L
L
b
a
q
2
La
La
p
L H
L H
bb
aa
>>
∑
∑−=
−=
i
iL L L L
i
iH H H H
qba p
qba p
Oligopoly
L L L L
H H H H
qba p
qba p
Monopoly
−=−=
H
H
b
a
2 H
H
b
a q
H a
2
H a
p Low fare High fare
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Two fares: Monopoly vs Competition (2 airlines)
H
L H
b
aa −2
1 C
La5.
H a
H a5.
La
p
+ H
H
L
L
b
a
b
a
2
1
H p
L p
Fare not offered
∆
H
L H
b
aa −3
2 C
3/ La
H a
3/ H a
La
p
+
H
H
L
L
b
a
b
a
3
2
L
H
p
p
Fare not offered
p∆
j j
j
j j
j j
j j
j
j j
j
j
bb
C b
aa
a p
bb
C b
aa
bq
−
−
−
−
−
−
+
+−
−=
+
+−
=
11
2
1
11
2
1
1
j j
j
j j
j j
j j
j
j j
j
j
bb
C b
aa
a p
bb
C b
aa
bq
−
−
−
−
−
−
+
+−
−=
+
+−
=
11
3
2
11
3
2
2
1
Monopoly Competition
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17
Competition leads to:
IncreaseDecrease(usually)
Quantity
DecreaseIncrease
(usually)
Price
High FareLow Fare
Average price - DECREASE
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Multiple fares/Multiple airlines
J
J
bbbb
aaaa
jbyindexed fares J ibyindexed airlines I
>>>>
>>>>
...
...
311
321
C
2a
5a
p
5
4
3
2
1
p
p
p
p
p
1a
3a
4a
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Solution for Multiple Airlines/Multiple Fares
∑
∑
∑
∑
∑
−
=
−
=
−
=
−
=
=
+−+−=
+−
+×
=
<−
+
1
1
1
1
1
1
1
1
1
1
1
1
11
.
1
:
M
k k
M
k k
k j
j j
M
k k
M
k k
k j
j
j
M
j j
M j
b
C b
aa I
I
a p
b
C b
aa
I
I
b I q
closed are J throughM Fares
C b
aa
I
I
that suchM highest Find
As degree of competition increases:
Average price goes down
Load factor goes upHigh fare prices go down
Low fare prices may go up
Price differences decrease
Fewer low fares are open
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Summary
Competition affects revenue management!
Competition is an important factor to consider
When prices are fixed competition leads to …
•Increase in high-fare seats and decrease in low-fare seats
When prices are decision variables competition leads to …
•Decrease in average prices BUT low fares may go up
In both cases airlines focus MORE on high-fare seats under
competition.