The University of Adelaide
School of Economics
Research Paper No. 2006-06
Intertemporal Price Discrimination and
Competition
Ralph-C Bayer
Intertemporal Price Discrimination
and Competition
Ralph-C Bayer
School of Economics, University of Adelaide†
Abstract
In this study we investigate the impact of competition on markets for non-durable goods where intertemporal price discrimination is possible. We develop a simple model of di#erent potential
scenarios for intertemporal price discrimination and implement
it in a laboratory experiment. We compare the outcomes in monopolies and duopolies. Surprisingly, we %nd that competition
does not necessarily prevent intertemporal price discrimination,
as our model predicts. However, competition generally reduces
sales prices, but by far less than theory predicts. As expected,
competition increases e'ciency.
Keywords: Price Disrcrimination, Oligopoly, Market Experiments
JEL Codes: L12; L13; C91
Introduction
Some econometric evidence suggests that the extent of price dispersion
in markets for non-durable goods - such as airline tickets and perishable
commodities - does not negatively depend on the competitiveness of the
market, as basic intuition would suggest. Stavins (2001) and Borenstein
& Rose (1994) even %nd that competition increases price dispersion.
School of Economics, University of Adelaide; Tel.: ++61-8 8303.4666; fax:
++61-8 8323.1460.
E-mail address: [email protected]
†
I wish to thank the Facilty of Professions at the University of Adelaide for funding
under the Faculty Research Grant scheme. I am also grateful for helpful comments
from John Hatch, Ludevic Renou and seminar participants at various instituions. I
am indebted to Nick Robinson for great IT support, to Yang Shen for very valuable research assistance, and to Timothy Bridgeman from Vigin Blue Australia for
providing me with some insight into the pricing strategies of Virgin Blue.
1
There are a variety of possible reasons for the persistence of intertemporal price dispersion in competitive markets. Candidates o#ered in the
literature are repeated interaction, demand uncertainty, capacity constraints or costly buyer search. Price dispersion can be discriminatory,
i.e. customers with di#erent preferences pay di#erent prices, or the consequence of real cost di#erences. These two cases are hard to disentangle,
as anti-trust cases have repeatedly shown. For example airline tickets
that are purchased well in advance are usually cheaper than tickets that
are bought close to the departure date. This can be interpreted as intertemporal price discrimination, as holiday makers with low reservation
prices purchase in advance, while business travellers with high reservation prices buy close to the time of departure. However, it can also be argued that the di#erent ticket prices just reBect real cost di#erences. Lott
& Roberts (1991) argue that the higher price for late bookers includes
the opportunity costs of the airline’s risk of having empty seats. They
also argue that price dispersion cannot be discriminatory, since competition and low search cost prevent pricing above marginal cost. So can
we conclude that all intertemporal price dispersion in markets for nondurables with more than one %rm, can only be due to cost di#erences?
An increasing body of theoretical literature suggests that this conclusion
is not valid, as it shows that under certain circumstances intertemporal
price discrimination is possible even in competitive non-durables markets.1 Some kind of uncertainty, capacity constraints and/or repeated
interaction are the necessary ingredients for models where intertemporal
price discrimination for non-durables prevails under competition.2
Gale (1993) shows in a model, where consumers ex ante do not know
which variety of a good they prefer, that the price dispersion between
advance-purchase prices and spot prices is higher in a duopoly than in
a monopoly. The results are driven by the uncertainty, which implies
that goods are ex ante homogeneous, but become di#erentiated once the
consumers have learned their preferences. So ex post there is some scope
for price discrimination. Dana (1998) shows that market segregation of
low and high-valuation customers can be achieved by competitive %rms
if capacity is costly and there is some correlation between individual
valuations and demand uncertainty. In a model with durable goods Sobel
(1984) shows that price cycles (high prices with periodical discounts) are
an equilibrium even when there are multiple %rms selling an homogenous
1
Elmaghraby & Keskinocak (2003) provide a comprehensive overview over current
dynamic pricing practices. Both cost and discrimination are shown to be reasons for
%rms changing prices over time.
2
The potential existence of static inter%rm equilibrium price-discrimination was
%rst outlined in Prescott (1975) and formalised by Eden (1990).
2
good. The discounts are used to get low-valuation customers to buy and
%rms make supernormal pro%ts. The main reason why the Bertrand logic
of undercutting does not necessarily apply in durable goods markets is
that repeated interaction gives rise to trigger strategies which support
an equilibrium with price cycles. This logic can easily be extended to
%rms who compete repeatedly in subsequent non-durable goods markets.
Burdett & Judd (1983) and Stahl II (1989) show that price dispersion
can prevail under competition if consumers’ costly search creates some
demand uncertaincy.
In this paper we test experimentally whether intertemporal price
discrimination really disappears with competition if we use a very simple
framework that does not exhibit any of the characteristics that were
used to theoretically explain price di#erntiation. Put di#erently: are
there any behavioural reasons why we might observe intertemporal price
discrimination even when the competitive environment appears to favour
the law of one price? Alternatively, are there potential reasons why we
should not observe price discrimination even when is a monopolist seller?
A potential behavioural factor that mitigates the pressure of competition towards a stable sales price is the limited depth of iteration
exhibited by consumers. To see this, put yourself in the shoes of a consumer who wants to purchase an airline ticket. Assume for instance that
you know that there are more seats than potential travellers. You check
the ticket prices of the di#erent operators continuously on the web. For
the Bertrand logic to work, i.e. price undercutting down to marginal
cost without any sales at prices above marginal cost, consumers have to
anticipate and to be sure that %rms will eventually undercut each other.
Consumers also have to be sure that the other customers also know this
and will act accordingly. For certain conjectures about the behaviour of
the other market participants it becomes optimal for a customer to buy
in advance and at a price above marginal cost.
On the other hand, fairness considerations could explain why a monopolist loses some of his price-discrimination power. Suppose your plan
to By develops at short notice. From experience you know that the price
will be quite high and would have been much lower if you booked earlier. If you are spiteful about the unfairness of the monopolist trying to
extract a very high proportion of the surplus just because you decided
spontaneously to By, then your reservation price given the pricing policy
of the airline might be lower than your valuation of the Bight. You %nd
the pricing of the monopolist unfair and are willing to forgo the bene%t of
travelling rather than be exploited by the airline. So you might call the
price "ridiculous" and abstain from travel even though the price is below your valuation. Preferences like these limit the price-discrimination
3
power of a %rm regardless of market power.
We experimentally implemented two typical market environments
where theory predicts that in equilibrium a monopolist can price discriminate, while duopolists cannot and compared the outcomes for monopolies and duopolies. We call these environments last-minute discounting
and early-bird discounting. In both cases the typical Bertrand logic
applies for markets with more than one %rm and price discrimination
should not be observed in equilibrium.
In the last-minute discounting scenario the intuition as to why a monopolist can price discriminate is similar to that in Dudey (1996). A
market where posted prices can be revised many times before the nondurable good is delivered (or perishes) allows a monopolist to sell at
(or just below) the monopoly price initially, in order to revise the price
downwards later on. Consumers, which are heterogenous in there valuation, anticipate that the price will never fall below the monopoly price,
if nobody buys early. So at least one consumer with a high valuation
is willing to accept early.3 Then once the %rst high-valuation customers
are out of the market the monopolist can charge the now decreased
pro%t maximising price to the remaining low valuation customers. Such
a pricing strategy is pro%table, since consumers with valuations below
the static monopoly price now generate revenue, while the consumers
with higher valuations self-select and buy at the static monopoly price.
Our experiments reveal that in the last-minute scenario duopolists do
not achieve any intertemporal price discrimination. Surprisingly, the
monopolists have severe problems, too. Monopolists are only sometimes
able to price discriminate and hardly do any better in terms of pro%ts
than the duopolists.
The second scenario is the commonly observed early-bird discounting situation. When customers with lower valuations for the good start
searching earlier for cheap prices than consumers with higher valuations
then it is possible to sell to these customers at early-bird discount prices,
while the high valuation customers who enter later can be charged higher
prices. The main objective of the monopolist is to get the low-valuation
customers out of the market before the high-valuation customers arrive.
The low-valuation customers accept early, as they anticipate that the
prices will go up over time. We observed that the experimental monopolists were able to price discriminate quite regularly. Surprisingly, the
3
In our case where a consumer only wants to buy one unit the high valuation
customers are indi#erent between buying early at the monopoly price or waiting.
The monopolist can break the tie by lowering the price slightly. In Dudey’s model
high-valuation customers prefer buying early, as that will guarantee lower prices for
addtional units in the future.
4
duopolists were able to do so, too. Comparing the frequency of successful
price discrimination even suggests that duopolists were more successful;
but monopolists achieved higher prices than duopolists, whenever they
were able to price discriminate. Over all, the monopolists did not make
higher pro%ts though, as they quite often were confronted with spiteful
consumers who did not buy at all. The refusal of some customers to
accept prices, which were high but still below the valuation, hurt the
monopolists pro%ts.
The reminder of the paper is organised as follows. Sections 1 and
2 lay out the two market environments and characterise the equilibria
for monopolies and duopolies. Section 3 brieBy discusses the crucial
behavioural assumptions necessary for the polarly di#erent equilibrium
predictions for duopolies and monopolies, while section 4 describes the
experiment. In section 4 the experimental results are presented. Section
6 concludes.
1
Last-minute discounting
One well known phenomenon in dynamic pricing is discounting such
as last-minute pricing in travel industries. Discounting can be used by
monopolists as an instrument for intertemporal price discrimination. We
use a simple example in order to demonstrate how such discounting
works. Suppose we have two consumers - denoted by 1 and 2 - with
di#erent valuations (v1
v2 ) for one unit of an homogeneous good.
The valuations, but not the identities of the consumers, are common
knowledge. There are N %rms which sell the good. For simplicity assume
that %rms are identical and have zero marginal cost. The set of %rms is
denoted by K. The consumers enter the market at period t0 = 1 and the
market has a %nal date T. After period T the good is worthless, just like
an airplane ticket once the plane has left. In each period t {1, 2, ..., T }
the %rms simultaneously set their prices pk (t). Consumers observe the
prices and decide to buy from a speci%c %rm or to wait. Denote the
decision to buy or not from %rm k in period t as ai (t, k), with ai (t, k) = 1
indicating a purchase and ai (t, k) = 0 indicating a non-purchase. Ex post
payo#s for the consumers are given by:4
T
N
Vi =
ai (k, t) (vi
pk (t))
(1)
i = 1, 2
t=1 k=1
The %rm’s ex post pro%t is given by:
T
k
2
=
(2)
ai (k, t)pk (t) i = 1, 2.
t=1 i=1
4
Note that a consumer only wants to buy one unit of the good (
5
t
k
at,k = 1).
Suppose that %rm’s only observe their own sales and the past prices
of their competitors. Consumers only observe their own purchases. First
observe that for N > 1 intertemporal price discrimination is never an
equilibrium. The usual Bertrand logic of undercutting applies.
Proposition 1 For N > 1 in the last-minute setting we have
2
ai (k, t)pk (t) = 0 t
i=1
{1, 2, ..., T }, k
K.
Proof. For each period and history a %rm has to have beliefs about
which customer is still interested. Suppose that in period T at least two
%rms believe that there is a positive probability that there is at least one
remaining consumer. Then pk (T ) = 0 for at least two %rms. Otherwise
there is a pro%table deviation. Note that the remaining customer will
accept the lowest price in T. If pmin (T ) = mink [pk (T )] > 0 then at least
one %rm j has a pro%table deviation by posting pj (T ) = pmin (T )
.
Suppose that pmin (T ) = 0 for only one %rm j with pk (T ) > 0 for all k = j,
then %rm j has a pro%table deviation by posting a price pmin (T ) + .
Beliefs have to be consistent in equilibrium, which implies that if there
is still an interested customer all %rms must assign a positive probability
to this. Therefore mink [pk (T )] = 0 if there is still a customer in the
market. Anticipating this, consumers will never buy for prices above 0
in earlier periods. So either ai (k, t) = 0 or pk (t) = 0.
The proposition above shows that there is no scope for pro%table intertemporal price discrimination in a dynamic Bertrand Oligopoly. We
now turn to the monopoly case. A monopolist who cannot price discriminate will be able to achieve a monopoly pro%t. As the game is a kind
of ultimatum game the monopolist has all the power. So he can always
charge and implement the unitary monopoly price pM :5
pM = arg max
p
M
=
M,
with
0 if p > v2
p if v2 p > v1
2p if p v1
Therefore the monopoly price depends on the valuations. Sometimes it
pays to charge a price which leads to both consumers buying the good.
Sometimes the monopolist only wants to sell to the high-value customer:
pM =
5
v2 if v2
v1 else
2v1
We implicitly assume that an indi#erent consumer accepts.
6
We now ask if the monopolist can do better than the monopoly pro%t if
he has the option to charge di#erent prices over time. This is possible
if v2 2v1 . Then the monopolist can force the high-valuation customer
into early acceptance at price p = v2 (or v2
), while he can charge
the low-valuation customer p = v1 later. Denote the point in time when
the high valuation customer accepts as t and the period when the lowvaluation customer accepts as t, respectively. Then we can state the
following proposition.
Proposition 2 If v2 2v1 then t < t, pM (t) = v2 , pM (t) = v1 , pM (t)
v2 for t t, and pM (t) v1 for t < t t describe equilibrium price paths
in the last-minute discounting case.
Proof. For the high-value customer any price above v1 clearly indicates
that the low-valuation customer will not accept. A high-valuation customer not accepting in the penultimate period will induce the monopolist
to charge pM (T ) = v2 . Not accepting in earlier periods t will trigger
prices pM (t) v2 in t where t < t < T. Therefore the high-valuation customer will accept if pM (t) v2 . The low-valuation customer will always
- independent of beliefs - accept a price pM (t) = v1 , as she anticipates
that it is never optimal for the %rm to charge a lower price. Given this
strategy of the consumers a price path characterized above is optimal
for the monopolist, as he extracts the maximum surplus v1 + v2.
Note that if v2 < 2v1 intertemporal price discrimination is not feasible
if consumers make no mistakes. A high-valuation customer will never
accept a price above pM = v1 , as she knows that this will be the price
charged if both consumers stay in the market until the last period. The
low-valuation customer will never accept a price above v1 , since this is
a dominated strategy. Both units will be sold at the static monopoly
price.6
Typical examples of pricing following a pattern described in the
proposition above are last minute-pricing (for airline tickets, products
sold at fruitmarkets just before closing, or during end of season fashion
sales),or high introductory prices for books (hardbacks vs. paperbacks),
movies (cinemas vs. DVD rentals) or electronic gadgets. The keen, impatient consumers buy early at a high price, while the less keen and more
patient consumers purchase later at a lower price.
2
Early-bird discounting
In some other instances we see that the prices in dynamic markets do
not decrease but increase over time. There might be many reasons for
6
If consumers have a downward-sloping demand for more than one unit price
discrimination is possible for less extreme valuations.
7
such a pricing policy. Early bookings for example reduce uncertainty for
airlines, who might be willing to forgo some pro%t in order to reduce this
uncertainty. Introductory pricing in markets with network externalities
might be another reason. Here we want to investigate intertemporal price
discrimination between di#erent customer groups, who enter the market
at di#erent points in time. One might think of holiday makers versus
business travellers in the market for airline tickets.7 Holiday makers
usually plan ahead and enter the market for a particular Bight quite early,
while business travellers often cannot plan well in advance. Additionally,
the reservation price of business travellers is much higher than that of
holiday makers. A monopolist airline will try to persuade as many lowvaluation customers as possible to book early, such that it can charge
higher prices later when the high-valuation customers have entered the
market.8
We can use our simple framework from above to investigate earlybird discounting. We again have two consumers with di#erent valuations,
v2 > v1 . Now assume that only the low-valuation customer enters the
market at t0 = 1, while the high-valuation customer only starts looking
for a ticket at t̂, with 1 < t̂ T. Again, the distribution of the privately
known valuations and the timing are common knowledge. As in our
previous setting, there is obviously no scope for price discrimination if
there is more than one %rm.
Proposition 3 For N > 1 in the early-bird setting we have
2
ai (k, t)pk (t) = 0 t
i=1
{1, 2, ..., T }, k
K.
Proof. The proof is analogous to that of proposition 1.
In a monopoly price discrimination is certainly possible. Denote
the point in time when the low valuation customer accepts as t and
the period when the high-valuation customer accepts as t, respectively.
Then, assuming that an indi#erent consumer accepts, we can state the
following proposition.9
7
Another example are early-bird rates for parking space, blocks of discounted
tickets for sports and other events issued well in advance of the event.
8
Technically, airlines divide the seats on a Bight in contingents with di#erent
prices. Holiday makers buy the cheaper tickets, while these are sold out when the
business travellers book. Airlines also use other discrimination devices, such as conditions and restrictions on tickets which are only acceptable for non-business travellers.
9
This is just to break a tie. The alterntive assumption would result in equilibriumpurchase prices to be marginally lower. Allowing consumers to randomise if they are
indi#erent complicates the analysis, but does not lead to additional insights.
8
Proposition 4 For N = 1 in the early-bird setting, t < t̃, pM (t) v1
for t < t̃, pM (t) = v1 , and t
t̃, pM (t)
v2 for t
t̃, pM (t) = v2
characterise the equilibrium paths.
Proof. At any point in time the monopolist knows how many consumers
there are in the market, as he is the only seller. Given that there is
at least one consumer in the market in the last stage posting a price
below v1 is never sequentially rational since posting v1 will lead to all
consumers in the market accepting and raising the price to v1 therefore
increases the pro%t. This logic extends to period T
1, T
2, and
so on. Therefore a low-valuation consumer, given the assumption that
indi#erence leads to a purchase, will always accept a price of v1 . So
charging pM (t) v1 and pM (T ) = v1 at least once in the periods t < t̃
results in the low valuation customer buying. Then with customer 1
out of the market the monopolist can, independently of customer 2’s
beliefs about the presence of customer 1 in the market, force customer
2 to accept a price of pM (t) = v2 , as the game becomes an ultimatum
game (i.e. consumer 2 will always accept pM (t) = v2 in t = T ). A
monopolist can never improve on a pro%t of M = v1 +v2 , which extracts
all the surplus. So the pricing strategies guaranteeing this payo# are the
equilibria of the game.
3
Price discrimination and crucial assumptions
Our simple model gives very stark predictions. In both settings, a monopolist can perfectly price discriminate and earn the maximum pro%t
of v1 + v2 , while under competition the %rms have no scope for price
discrimination at all and earn zero pro%ts. Two commonly employed
assumptions are absolutely crucial for these stark predictions:
1. Players behave sequentially rational over all periods and know that
the other players also do so.
2. Fairness motives are absent.
Various (experimental studies) have shown that these assumptions
are often violated by individuals. Individuals seem to have problems with
sequential rationality already under perfect information (see for example
Brandts & Figueras (2003) or Selten (1978)). Furthermore, studies have
shown that individuals often believe that other individuals are not clever
enough to behave rationally(e.g. documented by Fehr & Tyran (2001))
and therefore best-respond to some anticipated non-optimal behaviour.
Moreover, the result of perfect inter-temporal price discrimination is
9
based on the ultimatum game logic. The failure of simple backwardinduction logic was %rst shown by (Guth, Schmittberger & Schwarze
1982). There responders are not content with pittances o#ered by the
proposers and frequently reject low o#ers, even if rejection means a payo#
of zero. Fehr & Schmidt (1999) explain this behaviour with inequality
aversion, where rejections are a means of reducing inequality, as they
enforce equality by destroying all surplus, leading to zero payo#s for
both the proposer and the responder.
If we relax the two assumptions a wide variety of behaviour in our
two dynamic pricing scenarios can be rationalised. If e.g. consumers in
the case of N > 1 believe that %rms will not undercut each other until
they arrive at a price of zero, acceptances of relatively high prices (maybe
even early in a market) become possible. Given that a consumer with a
high valuation is more prone to accept early (or that %rms believe that)
some price discrimination becomes possible in the last-minute scenario
with N > 1. On the other hand, if the high valuation consumer does not
foresee that a monopolist might charge a price close to his valuations
as long as both consumers are in the market then in the last-minute
scenario a monopolist might lose his price discrimination ability.
A further limiting factor for price discrimination by a monopolist
might work through inequality aversion. If the monopolist foresees that a
customer is willing to reject "unfair" %nal-round o#ers even if a purchase
would lead to a positive surplus then he may decrease the price in order to
ensure a sale. On the other hand, if consumers are willing to accept equal
splits of surplus immediately with positive probability, as suggetsed by
many ultimatum-game experiments, then there might be the chance of
price discrimination in markets with competition.10
Given that we believe that the behavioural assumptions above are not
necessarily valid we cannot predict whether competition really eliminates
(or at least reduces) inter-temporal price discrimination. To investigate
this question further we implement the two scenarios from sections 1 and
2 in the laboratory and compare actual behaviour in markets with one
%rm to that in markets with two %rms.
4
Experimental implementation
We used z-tree by Fischbacher (1999) to run nine sessions with a maximum of 24 participants each. Overall we had 190 participants. The
subjects were assigned to di#erent treatments (monopoly - early bird,
duopoly - early bird, monopoly - last minute or duopoly last minute).
10
Note that Fehr-Schmidt preferences alone are not su'cient for such behaviour.
Their formulation of inequality aversion would predict that proposer competition
rules out price discrimination.
10
Table 1 shows the treatments with the parameters, predicted purchase
prices (pi ) and acceptance periods (t, t). Recall that ti denotes the period when a consumer with valuation vi enters the market, T gives the
last trading period, and N is the number of %rms.
Early Bird
t1 = 1, t2 = 6, v1 = 75, v2 = 100
Last Minute
t1 = 1, t2 = 1, v1 = 45, v2 = 100
Monopoly
T = 10, N = 1
p1 = 75, p2 = 100
t 5<t
p1 = 45, p2 = 100
t<t
Duopoly
T = 10, N = 2
p1 = 0, p2 = 0
t t
p1 = 0, p2 = 0
t t
Table 1: Treatments and Predictions
Within a treatment subjects were randomly assigned a task (seller
or buyer). Subjects were grouped randomly - two buyers with one seller
in the monopoly treatments, two buyers with two sellers in the duopoly
treatments. In each market one buyer was assigned the high valuation
v2 , the other buyer was given the low valuation v1 . Subjects played ten
markets within the same group and role. At the end of the experiment
subjects %lled in a questionnaire with some questions concerning demographic variables. At the end subjects were paid contingent on their
performance, where the performance measure for subjects was the pro%t
for sellers and the net bene%t for buyers. On average the subjects earned
approximately 12 Australian Dollars for 50 minutes of their time.11
Each of the ten markets consisted of a maximum of ten trading periods. The number of %rms, valuations of the consumers and entry dates
were common knowledge. Each period the %rm(s) posted prices for the
good. Then the consumers, who were in the market at that time, decided which price - if any - they wanted to accept. After accepting an
o#er the consumer left the market. Firm(s) observed acceptances, but
not the valuation of the accepting consumer, while the consumers were
not informed about the decisions of their fellow consumer. Once the ten
trading periods where over or both consumers had accepted an o#er the
market ended.
According to the propositions in the previous sections theory predicts perfect inter-temporal price discrimination in a monopoly with zero
consumer surplus, while a duopoly should prevent price discrimination
resulting in zero pro%ts. Note that even though the market game has a
variety of equilibria, we do not have to be concerned with repeated game
11
Before the ten markets subjects were given some other unrelated decision tasks
on %nancial and health risk. They earned extra money for these tasks.
11
e#ects. The equilibria in the market game all have the same payo#s and
sale prices, only the timing and the behaviour o# the equilibrium path
di#er. Therefore the supergame (consisting of the ten markets) does not
have any equilibria, where the stage-game outcome di#ers from that of
the stage game equilibria. In the monopoly treatments the monopolist
in equilibrium can always enforce the maximum payo# in the last stage
game. All stage game equilibria lead to this maximum payo#. Therefore
using the backward-induction logic we can conclude that all equilibria in
the supergame lead to the full discrimination payo# in the stage games.
The same logic applies for the duopoly case, where the consumers achieve
maximum surplus in each stage game equilibrium.
5
Experimental Results
In what follows we analyse the behaviour in our experimental sessions.
First we compare the monopoly treatments with the duopoly treatment
with respect to sales prices and purchase periods. This will allow for
a conclusion about whether competition reduces inter-temporal price
discrimination. Then we turn to the question of welfare, where we compare the surplus generated in the monopoly with that generated in the
duopoly treatments. Finally, we turn to distributional questions by investigating the determinants of consumer and producer surplus.
5.1
Intertemporal price discrimination and competition
We %rst investigate under which scenario and treatment intertemporal
price discrimination occurs and whether competition reduces the occurrence of price discrimination. We begin with the early-bird treatments.
5.1.1
Early bird
Recall that in the early-bird scenario a monopolist in equilibrium price
discriminates by selling early to the low-valuation customer before the
high-valuation customer enters the market. Then he can force the high
value customer - with the low value-customer out of the way - to accept
a high price. Figures 1 and 2 (on page 14) depict the development of
the median accepted prices by the high and low-value customer (p1 and
p2 ) over the ten markets for the monopoly and the duopoly treatment.
We %nd that the median price accepted by the high-value customer exceeds the price accepted by the low-value customer in all periods in
both treatments. This points in the direction of intertemporal price
discrimination in both cases. However, the di#erence is that the prices
decrease with repetition in the duopoly treatment. The two straight
lines in the diagrams represent the equal split of surplus between con12
sumers and %rm(s). For the high-value customer (v2 = 100) the equal
split is at p = 50, while equal surplus sharing for low-value customers
(v1 = 75) is achieved with p = 37.5. In the monopoly treatment the
median prices are very close to the equal split in all ten markets. This is
very surprising as this is exactly what we would expect in two separate
ultimatum games.12 So in the monopoly treatment we seem to observe
inter-temporal price discrimination which takes into account the fairness
norms of the customers. In the duopoly treatment median prices start
o# close to the equal split and are driven down with experience without
ever reaching the competitive prediction of p = 0. Additionally, the high
value customers’ median accepted prices are still above those accepted
by the median low-value customer, which could be interpreted as the
persistance of intertemporal price-discrimination.
Price
Median Trading Prices (Early-Bird Monopoly)
55
50
45
40
35
30
25
20
15
p1-monopoly
p2-monopoly
1
2
3
4
5
6
7
8
9
10
Period
Figure 1: Development of the median trading prices (monopoly) over
the 10 markets
The %gures give an idea of the presence of intertemporal price discrimination in both treatments. A more comprehensive test has to be
conducted on the individual level. Successful inter-temporal price discrimination in the early-bird treatment should satisfy two conditions: 1)
p2 > p1 and 2) t < t. This allows for fairness preferences, as we do not
require the prices to be equal to the valuations. Given this de%nition
we pool the data obtained in the early-bird treatments and report the
frequencies in table 2.
12
See Camerer (2003), chapter 2 for an overview of the results of various ultimatumgame experiments.
13
Price
Median Trading Prices (Early-Bird Duopoly)
p1-duopoly
55
50
45
40
35
30
25
20
15
p2-duopoly
1
2
3
4
5
6
7
8
9
10
Period
Figure 2: Development of the median trading prices (duopoly) over the
10 markets
Monopoly
Duopoly
Total
Price discrimination
not successful successful
83
57
64
56
147
113
Total
140
120
260
Table 2: Frequency of successful price discrimination (early bird)
The frequencies are surprising. Duopolists seem to be more successful
at achieving price discrimination. A chi-squared test for independence
of the rows and columns reveals (p = 0.334, two-sided) that there is no
signi%cant di#erence between the two treatments. If we assume (as null
hypothesis) that in the absence of price discrimination acceptance prices
and acceptance stages are random and independently distributed where
the distributions of the acceptance prices (p1 and p2 ) and the acceptance
stages are pairwise identical, then we can test for inter-temporal price
discrimination in the two treatments. Under the null hypothesis the
fraction of successful (coincidental) price discrimination should be .25.
A binomial test reveals that the fraction of successful price discrimination is signi%cantly higher than .25 (p < 0.001) in both treatments. A
closer look at the trading periods where di#erent customers accept (Figure 3) reveals two regularities. First, in both treatments a high fraction
of the high-value customers accept before the low-value customers enter
the market in stage 6. This is an indication of successful inter-temporal
14
price discrimination. Secondly, the acceptance stage patterns are similar
across the two treatments, which shows why the extent of price discrimination does not signi%cantly di#er between the duopoly and monopoly
treatments.
Duopoly
20
0
10
Pe rcen t
30
40
Monop ol y
0
5
10
0
5
10
a cce ptance sta ge for lo w-v alu ation cu sto me r (early bird )
Graphs by Treatment
Duopoly
20
0
10
Percent
30
40
Monop ol y
4
6
8
10
4
6
8
10
a cce ptance sta ge for hi gh- valuation cu stom er (ea rly bird)
Graphs by Treatment
Figure 3: Acceptance stages in the early-bird scenario
5.1.2
Last minute
In the last-minute treatments theory predicts that the monopolist will
force the high-value customer to accept early and will then charge the
low-value customer her reservation price later. The %gures below show
the median accepted prices in the last-minute treatment for the ten markets.
Figures ?? and ?? show that high-valuation customers paid higher
prices than low-valution customers in the monopoly treatment, while
trading prices are roughly equal for both types of customers in the
duopoly treatment. In contrast to the early-bird scenario, a duopolist
is not able to charge the high-valuation customer more than the lowvaluation customer. This suggests that here (if at all) inter-temporal
price discrimination is only possible for a monopolist.
Table 3 reports the frequencies of successful price discrimination.
The duopolists achieved price discrimination in only about one fourth
of the markets. The monopolist had more success, but the di#erence
15
Median Trading Prices (Last-Minute Monopoly)
45
40
Price
35
30
25
p1-monopoly
p2-monopoly
20
15
1
2
3
4
5
6
7
8
9
10
Period
Figure 4: Development of the median trading prices (monopoly) over
the 10 markets
Monopoly
Duopoly
Total
Price discrimination
not successful successful
90
50
88
32
178
82
Total
140
120
260
Table 3: Frequency of successful price discrimination (last minute)
is only weakly signi%cant (p < 0.06, one-sided chi-squared test). Using
the null hypothesis that prices and acceptances are identically and independently distributed, we can test whether there is any inter-temporal
price discrimination at all. A binomial test con%rms our initial intuition.
There exists signi%cant price discrimination in monopolies (p < 0.004)
but not in duopolies (p > 0.37). The di#erences in the two last-minute
treatments come from the fact that the duopolists were not able to start
with prices both high enough to deter the low-valuation customers from
buying early and at the same time low enough to lure the high-valuation
customers into early acceptance. Figure 6 reveals that the acceptance
pattern under a duopoly does not di#er between low and high-valuation
customers. To the contrary, the monopolist can charge initial prices high
enough for the low-valuation customers not to accept. Consequently,
many high-valuation customers accept early, while more than 55% of
the accepting low-valuation customers only do this in stage 10.
16
Median Trading Prices (Last-Minute Duopoly)
45
p1-duopoly
40
p2-duopoly
Price
35
30
25
20
15
1
2
3
4
5
6
7
8
9
10
Period
Figure 5: Development of the median trading prices (duopoly) over the
10 markets
5.2
Inter-temporal price discrimination dynamics
The tests above are only valid under some rather strict assumptions: the
absence of serial correlation within a group and the absence of treatment
speci%c time trends. In this section we use panel estimation to allow
for serial correlation and treatment-speci%c time trends. However, this
comes at a cost. We have to make assumptions on the distribution of
the error terms, which might be problematic with our small sample.
We estimate %xed-e#ect panel Probits for the two scenarios allowing for
a general time and a treatment-speci%c time trend.13 The dependent
variable is successful price discrimination as de%ned above.
The Probit estimation shows that our preliminary understanding
needs some correction when we control for serial correlation and treatmentspeci%c trends. In the early-bird scenario our observation that intertemporal price discrimination is observed slightly more often in the
duopoly treatment becomes weakly signi%cant. The reason for this is
that the downward trend in successful price discrimination in a duopoly
is absorbed by the interaction competition×period. So we can say that
the duopolists are initially better able to price discriminate, while this
e#ect is eroded over time, as the monopolists learn how price discrimi13
Omitting the treatment-speci%c time trend yields very similar results as the nonparametric analysis. The treatment e#ects are very week and generally not signi%cant.
17
Duopoly
40
20
0
Pe rcen t
60
Monop ol y
0
5
10
0
5
10
a cce ptance sta ge for lo w-v alu ation cu sto me r (last m inu te)
Graphs by t reat
Duopoly
40
20
0
Percent
60
Monop ol y
0
5
10
0
5
10
a cce ptance sta ge for hi gh- valuation cu stom er (last m inute )
Graphs by t reat
Figure 6: Acceptance stages in the last-minute scenario
nation can be achieved.14 We can con%rm that in the early-bird scenario
competition does not reduce the ability of %rms to price discriminate it rather enhances it.
For the last minute treatment the results from the panel analysis
con%rm the results we obtained from the non-parametric tests. Competition reduces the ability to price discriminate considerably. However,
the gap between the two treatments is reduced over time.
5.3
Welfare
In our very simple setting in equilibrium all four situations should be
e'cient. Ine'ciencies only arise if customers do not buy the good. Why
should a customer reject an o#er in the last stage, when acceptance guarantees a positive payo#? In games with similar structure (like ultimatum
games e.g.) responders readily reject pro%table o#ers in order to punish
the proposer for making an unfair o#er. Rejection reduces not only the
own payo# to 0 but also wipes out any surplus for the proposer. So if
an individual wants to avoid disadvantageous inequality then rejection
becomes an option. We would expect - if there are rejections at all that most of them come from low-valuation customers in the monopoly
14
This interpretation comes from a positive trend for price discrimination in both
treatments, while the treatment-speci%c trend for the duopolist is negative.
18
discrim
early bird
last minute
N
Log pseudo-likelihood
P rob > 2
260
158.59
(< 0.01)
260
139.31
(< 0.01)
competition
0.73
(0.059)
1.34
(0.011)
competition×period
0.10
(0.083)
0.18
(0.007)
period
0.15
(< 0.001)
0.19
(< 0.001)
constant
1.08
(< 0.001)
0.53
(0.128)
0.11
(0.023)
0.41
(< 0.001)
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 4: Panel probit estimations of successful price discrimination
treatments. Low-valuation customers may perceive the same o#er as
much less fair than a high-valuation customer, as the relative surplus
distribution is much more skewed in favour of the seller if viewed from
the standpoint of the low-valuation customer. Additionally, we expect
competition to lead to downward pressure on the prices and therefore to
lower o#er prices, which are perceived as fairer and therefore result in
less rejections in the duopoly treatments.
Monopoly
Duopoly
Total
Early Bird
175 75 0
117 10 13
114 1 5
231 11 18
Last Minute
145 100 45
85
44
2
115
5
0
200 49
2
0
9
0
9
Total
280
240
260
Table 5: Welfare by treatment and scenario
Table 5 shows the experimental frequencies of di#erent levels of surplus by treatment and scenario. Surprisingly, we observe that in the
early-bird scenario rejections are more common among high-valuation
19
customers than among low-valuation customers (23 versus 13 in the
monopoly and 6 versus 5 in the duopoly treatment). This can be explained by the shorter amount of time the high-valuation customer has
to accept. In the last-minute setting we observe the expected pattern.
Low-valuation customers reject more often (53 versus 11 in the monopoly
and 5 versus 0 in the duopoly). This is easily explainable, as it becomes
optimal for the monopolist (where the lion’s share of rejections happen) to price the low-valuation customer out of the market, whenever
he cannot lure the high-valuation customer into early acceptance.
Clearly, competition increases welfare in our experiment, even though
that the underlying model does not predict this. Using the (pooled)
frequencies from above and conducting chi-squared tests con%rms this
suspicion: in both scenarios welfare is greater in the duopoly treatments
(p < 0.01 in both cases). We also ran random e#ect ordered Probits
in order to allow for correlation within markets. The non-parametric
results are con%rmed by the panel analysis.
5.4
Distributional analysis
We have seen that competition enhances welfare, even though it does
not perfectly eliminate price discrimination. Additionally, we neither
observe marginal-cost pricing in the duopolies nor monopoly pricing in
the monopolies. However, the analysis above has revealed that prices in
the duopolies are lower. Here we investigate the impact of competition
on distribution. Theoretically, the introduction of competition should
shift the surplus entirely from the sellers to the consumers. We do not
observe this extreme shift. However, there is a shift. We ran random
e#ect Tobit regressions for the joint consumer surplus of the customers.
The results are summarized in Table 6.
In both scenarios competition increases consumer surplus only with
experience. The treatment-period interaction is highly signi%cant. So
consumers bene%t from competition only in later periods.
We now turn to the sellers. There we would expect that competition
decreases the producer surplus (pro%t). We compare the pro%ts of the
monopolists with the joint pro%t the two duopolists achieve.
The results are surprising. In the early-bird scenario competition has
no inBuence on pro%ts. Even repetition does not bring the proftis closer
to the predicted zero-pro%t outcome. In the last-minute scenario competition even tends to increase pro%ts initially, while this e#ect is %rst
eroded and then overturned in later markets. The appropriate question
is the following. Why don’t monopolists make signi%cantly higher profits than duopolists, even though they achieve higher sales prices? The
reason is quite simple. The higher prices charged by monopolists lead
20
consumer surplus
early bird
last minute
N
Log pseudo-likelihood
P rob > 2
260
1197.56
(< 0.01)
260
1126.93
(< 0.01)
competition
11.43
(0.326)
1.49
(0.821)
competition×period
2.84
(0.017)
4.76
(< 0.001)
period
0.09
(0.915)
0.76
(0.177)
73.08
(< 0.001)
66.59
(< 0.001)
0.43
(< 0.001)
0.22
(< 0.001)
constant
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 6: Panel probit estimations of successful price discrimination
to more rejections. The pro%t enhancing e#ect of higher sales prices is
counteracted by the greater number of consumers not buying. However,
as consumers learn that the monopolists will not really react to rejections with lower prices in later periods, rejections become less frequent
and monopolists pro%ts increase.
6
Conclusion
In this paper we investigated the e#ect of the introduction of competition on market dynamics in settings where theory predicts that monopolists can price discriminate by changing posted prices over time, while
duopolists cannot. We experimentally implemented two scenarios. In
the early-bird scenario, the customer with the lower valuation for the
good enters before the high-valuation customer. Price discrimination
occurs when the low-valuation customer buys before the high-valuation
customer enters. In the last-minute scenario both customer enter at the
same time, while the valuations are so di#erent that price discrimination may occur when the high-valuation customer is lured into accepting
early.
We found that at least some price discrimination occurs in all but
the duopoly treatment of the last-minute scenario, even though theory
predicts no price discrimination in both duopoly treatments. In the
21
producer surplus
early bird
last minute
N
Log pseudo-likelihood
P rob > 2
260
1211.06
(0.209)
260
1125.22
(< 0.01)
competition
0.13
(0.326)
12.35
(0.079)
competition×period
1.90
(0.144)
2.95
(< 0.001)
period
0.50
(0.575)
0.53
(0.344)
73.33
(< 0.001)
59.83
(< 0.001)
0.23
(< 0.001)
0.30
(< 0.001)
constant
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 7: Panel probit estimations of successful price discrimination
monopoly treatments we %nd less price discrimination than expected.
Comparing the monopolists’ and the duopolists’ ability to price discriminate it is not clear that competition is actually harmful for the sellers.
In the early-bird scenario competition even seems to enhance the ability
to price discriminate initially, while with increasing experience this advantage is eroded. In the last-minute scenario we observe the opposite
e#ect. Competition per se eradicates price discrimination opportunities.
However, the monopolists loose their advantage with repetition.
Competition enhances e'ciency in the experimental markets. Welfare is lower than predicted in all four treatments, as buyers sometimes
deviate from the theoretical prediction by rejecting pro%table o#ers in
the %nal stage of a market. However, the e'ciency loss is much smaller
in the competitive treatments. The additional surplus created in the
competitve treatments is appropriated by the consumers. Lower sales
prices lead to increased consumer surplus in the duopoly treatments. In
contrast, the producer surplus (equal to the pro%ts) is roughly the same
in monopolies and duopolies. The higher sales prices in monopolies are
counteracted by more consumers refusing to buy.
In conclusion we %nd that the promotion of competition is bene%cial in markets where inter-temporal price discrimination is possible. It
substantially increases consumer surplus, without strongly reducing pro22
ducer surplus; but the bene%cial e#ect on consumer surplus is by far not
as strong as theory predicts. The monopolists had much less pricing
power than predicted by standard theory, while the duopolists - also
contrary to the prediction - were able to retain at least some pricing
power. The most striking advantage of competition is the increase in total welfare. In a situation where demand is perfectly inelastic, we would
not expect competition to have any positive inBuence on welfare; but it
does. Somewhat lower prices signi%cantly reduce the number of disgruntled customers, who boycott the sellers for reasons of inequaltiy aversion.
This (unexpected) welfare bonus renders competition a valuable force for
achieving better market outcomes, despite of the fact that competition
does not necessarily erradicate discriminatory price dispersion.
References
Borenstein, S. & Rose, N. L. (1994), ‘Competition and price dispersion in
the u.s. airline industry’, Journal of Political Economy 102(4), 653—
683.
Brandts, J. & Figueras, N. (2003), ‘An exploration of reputation formation in experimental games’, Journal of Economic Behavior &
Organization 50(1), 89—115.
Burdett, K. & Judd, K. L. (1983), ‘Equilibrium price dispersion’, Econometrica: Journal of the Econometric Society 51(4), 955—970.
Camerer, C. F. (2003), Behavioral Game Theory: Experiments in Strategic Interaction, Priceton University Press.
Dana, James D., J. (1998), ‘Advance-purchase discounts and price discrimination in competitive markets’, Journal of Political Economy
106(2), 395—422.
Dudey, M. (1996), ‘Dynamic monopoly with nondurable goods’, Journal
of Economic Theory 70(2), 470—488.
Eden, B. (1990), ‘Marginal cost pricing when spot markets are complete’,
Journal of Political Economy 98(6), 1293—1306.
Elmaghraby, W. & Keskinocak, P. (2003), ‘Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions’, Management Science 49(10), 1287—
1309.
Fehr, E. & Schmidt, K. (1999), ‘A therory of fairness, competition, and
cooperation’, Quarterly Journal of Economics 114, 817—868.
Fehr, E. & Tyran, J.-R. (2001), ‘Does money illusion matter?’, American
Economic Review 91(5), 1239—1262.
Fischbacher, U. (1999), z-tree - zurich toolbox for readymade economic
experiments - experimenter’s manual, Technical report, Institute
for Empirical Research in Economics, University of Zurich.
23
Gale, I. (1993), ‘Price dispersion in a market with advance-purchases’,
Review of Indutrial Organization 8, 451—464.
Guth, W., Schmittberger, R. & Schwarze, B. (1982), ‘An experimental
analysis of ultimatum bargaining’, Journal of Economic Behavior
& Organization 3(4), 367—388.
Lott, J. R. & Roberts, R. D. (1991), ‘A guide to the pitfalls if identifying
price discrimination’, Economic Inquiry 29(1), 14—23.
Prescott, E. C. (1975), ‘E'ciency of the natural rate’, The Journal of
Political Economy 83(6), 1229—1236.
Selten, R. (1978), ‘The chain store paradox’, Theory and Decision
9(2), 127—159.
Sobel, J. (1984), ‘The timing of sales’, The Review of Economic Studies
51(3), 353—368.
Stahl II, D. O. (1989), ‘Oligopolistic pricing with sequential consumer
search’, The American Economic Review 79(4), 700—712.
Stavins, J. (2001), ‘Price discrimination in the airline market: The e#ect
of market concentration’, The Review or Economics and Statistics
83(1), 200—202.
24