This study describes a spatial model of price discrimination in two-sided media markets. Given that media platforms offer a uniform price for consumers and either a uniform or discriminatory price for advertisers, we compare a platform’s profit and welfare under these two different pricing schemes. In contrast to the well-known result that price discrimination based on a consumer’s location leads to lower profits, if consumers have a strong aversion to advertising, we show that a platform’s profit is better off under price discrimination. In addition, if consumers rather dislike advertising, we show that price discrimination is detrimental to both a platform’s profit and the consumer’s welfare.

A media platform differs from traditional firms in that it has two revenue sources. One is advertising revenue, and the other is revenue from charging consumers. Moreover, in media markets, there are indirect network effects between advertisers and consumers. Advertisers receive *positive* network effects from consumers of the same platform because advertisers are interested in the number of consumers, which helps them to determine whether to place advertisements. However, consumers may dislike advertising. Therefore, advertisements in a media platform may yield *negative* network effects for consumers. Accordingly, media platforms adjust prices for advertisers and consumers to internalize these network effects.

Media platforms may be able to charge different agents different prices. The Economist, one of the most well-known weekly news magazines, price discriminates based on regions, sizes and colors in advertising rates. ^{[1]} For example, for the same sizes and colors, advertising rates in North America are more than twice that in the Asia Pacific region. Some Japanese newspaper publishers charge higher advertising fees for public firms than for private firms. Gil and Riera-Crichton (2011) investigated the Spanish TV market, in which TV stations price discriminate their advertisers and viewers. Moreover, publishing companies can sell advertising columns at different prices depending on the various characteristics of advertisers (such as industry and location). ^{[2]} The purpose of this paper is to consider whether this price discrimination in media markets is beneficial for media platforms, consumers and advertisers.

Oligopolistic price discrimination on the Hotelling model has previously been studied by Thisse and Vives (1988), Bester and Petrakis (1996) and Liu and Serfes (2004). ^{[3]} These analyses of price discrimination without indirect network effects suggest that a firm’s profit from price discrimination is below that from uniform pricing. ^{[4]} When a firm can price discriminate to account for a given rival’s prices, the firm extracts a surplus from local consumers. However, the firm sets low prices for distant consumers. Conversely, when a rival firm uses the same price schedule, price discrimination exacerbates competition; therefore, consumers benefit when firms engage in price discrimination. We examine how these well-known results change in media markets.

To investigate a spatial model of price discrimination in two-sided media markets, we extend the perfect spatial price discrimination model developed by Thisse and Vives (1988). ^{[5]} Two platforms are located at each end of a line, and two groups of agents, advertisers and consumers, are uniformly located along the line. There are asymmetric network effects between these groups. We consider a sequential game in which platforms first set prices for consumers, and then for advertisers. The reason that consumers choose first is the accuracy of marketing. ^{[6]} Recent developments in information technology improve the accuracy of marketing. Therefore, publishers can strictly predict the number of copies or consumer market share. Media platforms compete for advertisers using these consumer data.

In the first stage, platforms offer uniform prices for consumers deciding to join a platform. Platforms cannot price discriminate among consumers, as consumers can resell magazines. ^{[7]} In the second stage, both platforms simultaneously offer prices for advertisers. If price discrimination is feasible, both platforms price discriminate for each advertiser. Otherwise, platforms offer uniform prices for advertisers.

As advertisers select a platform in the final stage, similar to one-sided markets, price discrimination reduces the platform’s profit from advertisers. However, platforms adjust uniform prices for consumers in response to network effects. As price discrimination intensifies price competition in the final stage, advertisers can easily shift to a platform with a large consumer market share. Therefore, network effects are more influential in determining a platform’s profit from consumers under price discrimination than under uniform pricing. As negative network effects relax price competition, if consumers strongly dislike advertisements, a platform’s profit under price discrimination is higher than that under uniform pricing.

We also investigate consumer surplus. If negative network effects are moderate, platforms cannot compensate for price competition for advertisers by extracting a surplus from consumers. Consequently, despite the finding that price discrimination leads to reduced platform profit, consumers are worse off when platforms employ price discrimination. ^{[8]}

Our paper relates to the literature on two-sided markets using the Hotelling framework. ^{[9]} The seminal work of Armstrong (2006a) investigates the role of elasticities of demand in two-sided markets. Anderson and Coate (2005) analyze competition between media platforms in the presence of asymmetric network effects. However, these studies are limited to uniform pricing for each group of agents.

The recent paper by Liu and Serfes (2013) analyzes a Hotelling model of price discrimination in two-sided markets with positive network effects. They demonstrated that price discrimination and strong network effects increase a platform’s profit under the condition that the price schedule is limited to a non-negative price. While their model is related to ours, we demonstrate that platform profits increase in the presence of negative network effects under certain conditions. ^{[10]}

The remainder of this paper is organized as follows: Section 2 presents the model. Section 3 analyzes the equilibrium outcomes. We check the robustness of our model in Section 4. Section 5 concludes the paper.

There are two homogenous platforms (1 and 2). Each platform is located at the end of a unit line. There are two groups of agents: advertisers (sellers, *S*) and consumers (buyers, *B*). Each agent is uniformly distributed along the unit line and selects only one platform. ^{[11]} To join the platform, each agent incurs transportation costs per unit of distance
*i* is
^{[12]} The greater the number of consumers that select platform *i*, the greater the number of advertisers that place advertisements on the same platform. However, we assume that consumers dislike advertisements. The utility of group *k*’s agent, who is located at distance

Platform *i*’s profit is

[1]
π
i
=
(
p
i
B
−
c
)
n
i
B
+
p
i
S
n
i
S
.

The platform faces marginal costs
The game is as follows: First, the two platforms simultaneously set a uniform price for consumers. Consumers decide whether to join platform 1 or 2. In the second stage, we consider two price regimes. Under the first, both platforms set uniform pricing for advertisers, and under the second, both platforms price discriminate among advertisers.

We consider that each platform charges uniform prices to both groups. In the second stage, each platform offers a uniform price for advertisers. The number of advertisers who join each platform is given by

[2]
n
i
S
=
t
S
+
b
S
(
n
i
B
−
n
j
B
)
−
(
p
i
S
−
p
j
S
)
2
t
S
.

Using the platform’s profit function and the number of advertisers, we derive the price for advertisers. Proposition 1 summarizes prices and profits

**PROPOSITION 1***When each platform charges uniform prices for both the groups, equilibrium prices and profits are determined as follows*:

[3]
p
i
U
P
S
=
t
S
,

[4]
p
i
U
P
B
=
c
+
t
B
−
b
S
(
2
t
S
+
b
B
)
3
t
S
,

[5]
π
i
U
P
=
t
S
+
t
B
2
−
b
S
(
2
t
S
+
b
B
)
6
t
S
.

Proof. See
Appendix. ■
In symmetric equilibrium, each platform has half the market share of each group. The market share of consumers is determined in the first stage. In the second stage, all advertisers receive the same network benefits

We assume that in the second stage, two platforms can price discriminate among advertisers. Then, platforms can observe the location of each advertiser. Each platform controls the territory near its own location, i.e., platform 1’s territory is

When platforms price discriminate, each platform’s profit

[6]
π
1
P
P
D
=
∫
0
(
t
S
+
b
S
(
n
1
B
−
n
2
B
)
)
/
2
t
S
t
S
(
1
−
2
x
ˆ
S
)
+
b
S
(
n
1
B
−
n
2
B
)
d
x
ˆ
S
+
(
p
1
B
−
c
)
n
1
B
,

[7]
π
2
P
P
D
=
∫
(
t
S
+
b
S
(
n
1
B
−
n
2
B
)
)
/
2
t
S
1
t
S
(
2
x
ˆ
S
−
1
)
+
b
S
(
n
2
B
−
n
1
B
)
d
x
ˆ
S
+
(
p
2
B
−
c
)
n
2
B
.

Proposition 2 summarizes prices and profits when each platform price discriminates for advertisers.

**PROPOSITION 2***When each platform price discriminates in the second stage, equilibrium prices and profit are determined as follows*:

[8]
p
1
P
P
D
S
=
t
S
(
1
−
2
x
S
)
,
p
2
P
P
D
S
=
0
,
i
f
x
S
≤
1
2
,

[9]
p
1
P
P
D
S
=
0
,
p
2
P
P
D
S
=
t
S
(
2
x
S
−
1
)
,
i
f
x
S
≥
1
2
,

[10]
p
i
P
P
D
B
=
c
+
t
B
−
b
S
−
b
S
b
B
t
S
,

[11]
π
i
P
P
D
=
t
S
+
2
t
B
−
2
b
S
4
−
b
S
b
B
2
t
S
.

Proof. See
Appendix. ■
Similar to the case of uniform pricing, network effects do not affect prices for advertisers. The equilibrium prices for advertisers are identical to those in Thisse and Vives (1988). Prices for consumers include terms stemming from network effects. These terms under price discrimination are qualitatively similar to those under uniform pricing.

We study the symmetric equilibrium prices with and without price discrimination to compare profits. First, we compare prices for advertisers in the second stage. As each platform sets symmetric prices in the first stage, each platform obtains one half of the consumers. There is no difference in an advertiser’s network benefits under the two pricing schemes. Therefore, prices for advertisers are identical to those in Thisse and Vives (1988) on one-sided markets. In the second stage, a platform is profitable when price discrimination is feasible for a given rival’s prices. However, the rival will perform the same action. Therefore, price competition for advertisers is more intense when platforms can price discriminate. In the second stage, uniform pricing is more profitable than price discrimination.

Next, we consider prices for consumers in the first stage. Suppose platforms offer a symmetric price to consumers. Then, platform 1 slightly reduces

We investigate how these two effects impact consumer prices under price discrimination.

**PROPOSITION 3***Price discrimination is more profitable than a uniform price, if and only if*

Proof. See Appendix. ■

When a consumer joins a platform, the consumer anticipates that the platform will attempt to attract more advertisers in the second stage. If consumers strongly dislike advertising, in the first stage, the consumer has less incentive to join the platform, because the feedback effect is larger than the direct effect. This implies that the consumer is price inelastic. Therefore, the platform sets higher prices for consumers. However, this effect is present under both price discrimination and uniform pricing. In addition to this effect, when the platforms can price discriminate, a platform (e.g., 1) can attract more advertisers when platform 1 obtains consumers from platform 2. However, platform 2 cannot reduce prices for advertisers located at the middle of the line due to marginal cost pricing. As a consequence, price discrimination reinforces the above effect. Therefore, consumer prices are higher under price discrimination than under uniform pricing.

In the Hotelling model of one-sided markets, price discrimination intensifies price competition (see Thisse and Vives 1988). However, in our model that considers two-sided markets, if the negative network effects are sufficiently large, a platform’s profit under price discrimination is higher than that under uniform pricing. ^{[16]} Our result extends the findings of Liu and Serfes (2013), who analyzed a spatial price discrimination model considering two-sided markets with positive network effects and non-negative prices. In their model, if positive network effects are strong and prices are required to be non-negative, the profit of a platform is greater under price discrimination. In contrast to their result, we can derive our result with asymmetric network effects and without price regulation.

Next, we consider welfare. As all agents participate in platform 1 or 2, both pricing schemes have identical total welfare, which is composed of a platform’s profit and agent groups’ surplus. Therefore, under the condition of Proposition 3, the sum of both agent groups’ surplus under price discrimination is lower than under uniform pricing. To determine which pricing schemes affect each group, we compare each group’s surplus under price discrimination with that under uniform pricing. When each platform charges uniform prices for both groups, advertiser and consumer surplus are as follows:

[12]
C
S
U
P
S
=
2
∫
0
1
/
2
α
S
+
b
S
2
−
t
S
−
t
S
x
S
d
x
S
=
α
S
+
b
S
2
−
5
t
S
4
,

[13]
=
α
B
−
c
+
b
B
2
+
b
S
(
2
t
S
+
b
B
)
3
t
S
−
5
t
B
4
.

Similarly, when both platforms price discriminate among advertisers, advertisers and consumers surplus are as follows:
[14]
C
S
P
P
D
S
=
α
S
+
b
S
2
−
3
t
S
4
,

[15]
C
S
P
P
D
B
=
α
B
−
c
+
b
B
2
+
b
S
(
t
S
+
b
B
)
t
S
−
5
t
B
4
.

When platform profit is lower under price discrimination than under uniform pricing, we compare agent groups’ surplus under uniform pricing with that under price discrimination. Then, we can derive Proposition 4.
**PROPOSITION 4***When platform profit under price discrimination is lower than that under uniform pricing*,

- (i)
the advertisers’ surplus under price discrimination is always larger than that under uniform pricing;

- (ii)
the consumers’ surplus under price discrimination is smaller than that under uniform pricing, if and only if

Proof. See Appendix. ■

The preceding studies on one-sided markets, such as Thisse and Vives (1988), reveal that price discrimination reduces a firm’s profits and improves consumer surplus. In contrast, our model finds that price discrimination is detrimental not only to a platform’s profit but also to consumer surplus. ^{[17]} If negative network effects are moderate, platforms cannot compensate for engaging in price competition for advertisers by extracting surplus from consumers. Consequently, despite that a platform’s profit under price discrimination is lower than that under uniform pricing, consumers are worse off when platforms employ price discrimination.

This result suggests that policy action is necessary for agents on two-sided media markets. In our model, competition authorities may approve not only consumer surplus but also a platform’s profit as a policy objective. Platforms set a uniform price for consumers, resembling resale price maintenance (RPM). ^{[18]} RPM is used to protect publishing culture. Therefore, a platform’s profit becomes one of the policy objectives. Under the condition of Proposition 4, price discrimination is detrimental to a platform’s profit and consumer surplus. Competition authorities should ban price discrimination for advertisers. However, it may be difficult to implement the policy, as advertisers negotiate on their prices in a closed-door room. In contrast, competition authorities can observe a platform’s profit and prices for consumers. When competition authorities notice low profits and high prices for consumers, they could infer large advertiser surplus. Then, competition authorities should examine the prices for advertisers to protect a platform’s profit and consumer surplus.

Our result also suggests that competition authorities do not always have to ban price discrimination for advertisers. Under the condition of Proposition 3, a platform’s profit under price discrimination is higher than that under uniform pricing. However, price discrimination for advertisers is harmful to consumers under the condition. If competition authorities prefer to protect platforms, they permit price discrimination for advertisers. If

In contrast to our result, Liu and Serfes (2013) demonstrate that when price discrimination reduces a platform’s profit, both groups’ welfare improves. In their model, as both agent groups simultaneously join platforms, the two network effects equally affect prices and profits. In contrast, in our model, consumers select platforms before the platforms offer prices to advertisers. Therefore, the two network effects differently affect prices and profits.

In this section, we discuss four important assumptions about our basic model to check its robustness. ^{[19]} First, network effects are asymmetric. In Section 4.1, we consider a model with positive network effects for both sides. Second, the agent groups sequentially select a platform. We extend our model to the simultaneous case in Section 4.2. In the simultaneous game, platforms can potentially set negative prices for agents by internalizing network effects. Third, platforms can price discriminate among advertisers. We adapt our model to include price discrimination on both sides in Section 4.3. Finally, we discuss multihoming in Section 4.4. After reviewing these assumptions, we find that the simultaneous game, discriminating on both sides and multihoming do not intrinsically affect our main result. Therefore, the assumption of asymmetric network effects plays a key role in our main results. Moreover, we can compare our model with that Liu and Serfes (2013) by relaxing our assumptions except for multihoming. ^{[20]} Therefore, negative network effects differentiate our model from theirs. Moreover, they limit the price schedule to a non-negative price. However, our model intrinsically permits negative prices.

In this subsection, we investigate how the direction of network effects affects our main result. We extend our basic model to include positive network effects for both groups, i.e., suppose that

We extend our model to a simultaneous game in which platforms set prices for consumers and advertisers simultaneously. We demonstrate that the results of this extension are qualitatively identical to those of the basic model.

First, we assume that platforms set uniform prices for both sides in the simultaneous game. This game is identical to that in Armstrong (2006a). Therefore, the equilibrium prices are

In the simultaneous game, platforms price discriminate among advertisers and set uniform prices for consumers. First, we consider prices for advertisers following Liu and Serfes (2013). Given platform 2’s prices for advertisers and consumer market share, platform 1 charges prices for advertisers who prefer platform 1 to platform 2:

We investigate platform 2’s prices for advertisers. For the advertisers who prefer platform 1, platform 2’s prices are equivalent to platform 2’s external benefit of attracting an additional advertiser. ^{[21]} When platform 2 attracts an additional advertiser, platform 2 loses a further
^{[22]}

Third, we explore the case in which platforms can price discriminate on both sides. In this extension, platforms sequentially attract both sides similarly to our basic model. As platforms set prices for advertisers in the final stage, the discriminatory prices for advertisers are identical to those in our basic model, i.e., eqs [8] and [9]. We consider discriminatory prices for consumers. Given the market share of advertisers, platforms select discriminatory prices for consumers near platform 1 as follows: ^{[23]}

In this extension, consumer surplus is as follows:

In this subsection, we consider the extension of our model in which advertisers have the possibility to multihome. Similar to the result of our basic model, we find that the platform profit under price discrimination rises when consumers strongly dislike advertisements. First, we consider the prices for advertisers when advertisers can multihome. Suppose that

In the basic model, we assume that

Next, we consider the case in which certain advertisers are singlehoming and other advertisers are multihoming. Then, the equilibrium prices for advertisers are

We compare platform profits from advertisers under price discrimination with those under uniform pricing. When advertisers can multihome under price discrimination, a platform can extract all surpluses from advertisers joining the platform. However, under uniform pricing, as each platform sets a monopoly price for advertisers, advertisers enjoy some surplus. Therefore, the platform profit from advertisers increases under price discrimination, which differs from the result of our basic model.

Next, we consider the prices for consumers in the first stage by adapting the intuition from Section 3. When platform 1 has an additional consumer, platform 1 has

We consider agents’ surplus when advertisers can multihome. In the singlehoming case, advertiser surplus is greater under price discrimination, because it produces fierce competition. However, in the multihoming case, advertiser surplus is lower under price discrimination. However, consumer surplus does not change qualitatively irrespective of whether advertisers multihome. When negative network effects are sufficiently low, consumer surplus is lower under price discrimination.

We have investigated a spatial model of price discrimination in two-sided media markets. The result is that if negative network effects are sufficiently large, a platform’s profit under price discrimination is higher than that under uniform pricing. We also demonstrate that platforms and consumers are worse off when platforms engage in price discrimination if negative network effects are moderate. This result concerning agents’ welfare indicates that policymakers may need to reconsider policies in two-sided markets.

We take a preliminary step in studying a model in which platforms can price discriminate on the locations of agents. In media markets, platforms can price discriminate on the size or quantity of advertising. The extension of our model to include second-degree price discrimination should be addressed in future research.

We consider prices for advertisers in the second stage. Using eqs [1] and [2], the first-order condition is

[16]
∂
π
i
U
P
p
i
S
=
t
S
+
p
j
S
−
2
p
i
S
+
b
S
(
n
i
B
−
n
j
B
)
2
t
S
=
0.

Solving these equations, we obtain prices for advertisers and the number of advertisers:
[17]
p
i
S
=
t
S
+
b
S
(
n
i
B
−
n
j
B
)
3
,
n
i
S
=
1
2
+
b
S
(
n
i
B
−
n
j
B
)
6
t
S
.

Next, we consider prices for consumers in the first stage. Using eq. [
17], the number of consumers who join each platform is given by
[18]
n
i
B
=
3
t
S
(
p
j
B
−
p
i
B
)
−
b
S
b
B
n
j
B
+
3
t
S
t
B
6
t
S
t
B
−
b
S
b
B
.

Therefore, we obtain the number of consumers:
[19]
n
i
B
=
3
t
S
(
p
j
B
−
p
i
B
)
+
3
t
S
t
B
−
b
S
b
B
2
(
3
t
S
t
B
−
b
S
b
B
)
.

Substituting eq. [
19] for prices for advertisers and the number of advertisers, platform’s profit is
■

We consider prices for consumers in the first stage. Since platforms charge uniform prices for consumers, the number of consumers is

[20]
n
i
B
=
t
S
(
p
j
B
−
p
i
B
)
+
t
S
t
B
−
b
S
b
B
2
(
t
S
t
B
−
b
S
b
B
)
,

[21]
n
i
S
=
b
S
(
p
j
B
−
p
i
B
)
+
t
S
t
B
−
b
S
b
B
2
(
t
S
t
B
−
b
S
b
B
)
.

Substituting eqs [
20] and [
21] for eqs [
6] and [
7], we can derive the first-order and second-order conditions:
■

We compare platform’s profits:

[22]
π
i
U
P
−
π
i
P
P
D
=
3
(
t
S
)
2
+
2
t
S
b
S
+
4
b
S
b
B
12
t
S
.

Therefore,
■

We compare consumer surplus using eqs [13] and [15]:

[23]
C
S
U
P
B
−
C
S
P
P
D
B
=
−
b
S
(
t
S
+
2
b
B
)
3
t
S
.

Therefore,
■

In this supplemental section, we provide a detailed analysis of Section 4. As it is easy to verify whether there exist positive network effects on both sides, we discuss three cases: a simultaneous game, discrimination on both sides and multihoming.

We extend our model to a simultaneous game and compare platform profits under uniform and discriminatory pricing. ^{[24]} In this extension, platforms simultaneously set prices for both groups. The main difference between the simultaneous and sequential games is the prices offered to advertisers. In the simultaneous game, platforms must account for the feedback loop created by the network effect in advertiser price. First, we explore the uniform pricing case in the simultaneous game, which is the same as that of Armstrong (2006a). Therefore, equilibrium prices and profits are

[24]
p
U
P
i
=
t
i
−
b
j
,

[25]
π
U
P
=
t
S
+
t
B
−
b
S
−
b
B
2
.

Next, we consider the case in which platforms simultaneously set discriminatory prices for advertisers and uniform prices for consumers.
[26]
p
1
S
=
t
S
(
1
−
2
x
S
)
+
b
S
(
n
1
B
−
n
2
B
)
+
p
2
S
,
f
o
r
x
S
≤
t
S
+
b
S
(
n
1
B
−
n
2
B
)
2
t
S
.

For
We explore platform 2’s prices for advertisers for
^{[26]} Therefore, platform 2’s total loss from obtaining an additional advertiser is

[27]
p
1
S
=
t
S
(
1
−
2
x
S
)
+
b
S
(
n
1
B
−
n
2
B
)
−
b
B
(
p
2
B
∗
+
2
b
S
(
1
−
x
S
)
)
t
B
,

[28]
p
1
S
=
−
b
B
(
p
1
B
∗
+
2
b
S
x
S
)
t
B
,

As

[29]
p
1
S
(
x
˜
S
)
=
−
b
B
(
p
˜
B
+
b
S
)
t
B
.

Moreover,
[30]
p
1
S
(
1
)
=
−
b
B
(
p
˜
B
+
2
b
S
)
t
B
.

Because
[31]
p
2
S
=
−
b
B
(
p
2
B
+
b
S
)
t
B
,
i
f
x
S
≤
x
˜
S
.

[32]
p
2
S
=
t
S
(
2
x
S
−
1
)
+
b
S
(
n
2
B
−
n
1
B
)
−
b
B
(
p
1
B
+
b
S
)
t
B
,
i
f
x
S
≥
x
˜
S
.

Next, we prove that platform 1 has no incentive to pursue other deviations: The first deviation is that platform 1 decreases its market share on the advertiser side by changing the price for advertisers located on
We also demonstrate that platform 1 has no incentive to pursue the second deviation. Suppose that the deviation price,

We investigate consumer prices. From eqs [31] and [32], platform 1’s profit is

([33]
π
1
P
D
=
∫
0
(
t
S
+
b
S
(
n
1
B
−
n
2
B
)
)
/
2
t
S
t
S
(
1
−
2
x
S
)
+
b
S
(
n
1
B
−
n
2
B
)
−
b
B
(
p
2
B
+
b
S
)
t
B
d
x
S
+
p
1
B
n
1
B
.

Because platforms set uniform consumer prices, the market shares of platform
[34]
∂
π
i
P
D
∂
p
i
B
=
−
t
S
+
t
S
b
S
(
p
j
B
−
p
i
B
)
t
S
t
B
−
b
S
b
B
−
b
B
(
p
j
B
−
b
S
)
t
B
b
S
2
(
t
S
t
B
−
b
S
b
B
)
+
t
S
t
B
−
b
S
b
B
+
t
S
(
p
j
B
−
2
p
i
B
)
2
(
t
S
t
B
−
b
S
b
B
)
=
0.

Solving the equations, the equilibrium prices and profit are
[35]
π
i
P
D
=
t
B
−
b
S
−
b
B
2
+
t
S
4
+
(
b
S
)
2
b
B
(
b
B
−
t
B
)
t
B
(
t
S
t
B
−
b
S
b
B
)
.

Note that
Finally, we compare profits under two different pricing schemes using eqs [25] and [35].

As the second-order condition holds, profits under uniform pricing are lower than under price discrimination if and only if

In this subsection, we extend our basic model to price discrimination on both sides. Platforms can price discriminate not only among advertisers but also among consumers. Analogously to the basic model, platforms sequentially set prices for both groups, i.e., consumers are charged in the first stage and advertisers are in the next. Suppose that
*i*’s market share on the consumer side determined in the first stage. Price discrimination among advertisers in this extension is the same in our basic model,

We investigate discriminatory prices for consumers. Suppose that a consumer at location

[36]
p
1
B
=
t
B
(
1
−
2
x
B
)
−
b
S
+
b
S
(
b
S
(
2
x
B
−
1
)
+
b
B
(
4
x
B
−
3
)
)
t
S
,

[37]
p
1
B
=
−
b
S
−
b
S
(
b
S
(
2
x
B
−
1
)
+
2
b
B
x
B
)
t
S
,

[38]
p
1
B
=
t
B
(
1
−
2
x
B
)
−
b
S
+
2
b
S
b
B
(
x
B
−
1
)
t
S
,

[39]
p
1
B
=
−
b
S
−
b
S
b
B
t
S
,

[40]
=
t
S
+
t
B
4
−
b
S
2
−
3
b
S
b
B
4
t
S
.

When platforms set these prices, they may have an incentive to pursue other deviations: The first deviation is that platform 1 contracts with more consumers on
[41]
π
1
P
D
d
−
π
1
P
D
=
−
b
S
δ
(
b
S
δ
−
b
B
)
t
S
>
0.

As the delta is sufficiently small,
[42]
p
1
B
=
t
B
(
1
−
2
x
B
)
−
b
S
+
b
S
b
B
(
2
x
B
−
1
)
t
S
,

[43]
p
1
B
=
−
b
S
,

[44]
π
1
P
D
=
t
S
+
t
B
4
−
b
S
2
−
b
S
b
B
4
t
S
.

Finally, we prove that platforms have no incentive to pursue the deviation in which platform 1 decreases its market share on the consumer side by changing the price for consumers located on
We compare the deviation profit with eq. [44]:

[45]
π
1
P
D
d
−
π
1
P
D
=
−
δ
2
(
t
S
t
B
−
b
S
b
B
−
(
b
S
)
2
)
t
S
<
0.

As
From our basic model, platform profits under uniform pricing are

We investigate the extension of our basic model in which advertisers have the ability to multihome. We explore the case in which certain advertisers singlehome and other advertisers multihome. Similar to the result obtained from our benchmark model, we find that platform profits under price discrimination are larger than under uniform pricing when negative network effects are sufficiently large.

The utility of an advertiser located in

We study the case in which platforms offer uniform prices to both groups. The locations of the marginal advertisers are given by

[46]
π
i
U
P
=
t
B
2
+
(
2
θ
+
b
S
)
(
2
θ
−
b
S
)
−
4
b
S
b
B
16
t
S
.

We consider the case in which platforms can price discriminate among advertisers. We identify the location

We obtain equilibrium prices, the number of agents and platform profit as follows:

[47]
π
i
P
D
=
t
S
+
t
B
−
2
b
S
−
2
θ
2
+
(
2
θ
+
b
S
)
2
−
2
b
S
b
B
4
t
S
.

Here, we investigate the extent to which
Comparing profits under uniform pricing and price discrimination, we find that platform profits are larger under price discrimination than under uniform pricing, if and only if

I would like to thank an editor and two anonymous referees, Hiroshi Aiura, Makoto Hanazono, Toshihiro Matsumura, and various seminar audiences for helpful comments. Financial support from AICA Kogyo is gratefully acknowledged.

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