Economics of Revenue Mgt Pricing Competition and Seat Allocation

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]



2

American

United

6:37

172 seats

6:05

108 seats

7:25

155 seats

21-day advance purchase round-trip: $289



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



3

“Horizontal” competition in US airline industry

From S. A. Morrison. 1998. “Airline Service: The evolution of competition since deregulation.”



4

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



5

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



6

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



7

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.



8

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



9

‘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.



10

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



11

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



12

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.



13

Fixed prices assumption

From S. A. Morrison and C. Winston. 1995. “The evolution of the airline industry.”



14

Evolution of prices

From S. A. Morrison. 1998. “The evolution of competition since deregulation.”



15

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



16

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



17

Competition leads to:

IncreaseDecrease(usually)

Quantity

DecreaseIncrease

(usually)

Price

High FareLow Fare

Average price - DECREASE



18

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



19

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



20

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.

Documents

Economics of Revenue Mgt Pricing Competition and Seat Allocation