User-Generated Content, Social Media Bias and Slant Regulation Jun Hu

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Jun Hu. User-Generated Content, Social Media Bias and Slant Regulation. 2021. hal-03120466v3

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Jun HU, University of Paris 2 Panth´eon-Assas

March 4, 2021

1 Contents

1 Introduction2

2 Related Literature4

3 The Model6

3.1 The Newspaper Market...... 6

3.2 Model Set-up...... 6

3.3 A Public-interest Newspaper Firm as an Instrument for Reg- ulation...... 9

4 The Equilibrium Analysis of a Location-price Game 10

4.1 Timing of the game:...... 10

4.2 The Market Shares...... 11

4.3 The Equilibrium Price Choices...... 12

4.4 The Equilibrium Reporting Positions and Slanting Strategies. 13

4.5 The Eﬀects of Slant Regulation on Equilibrium Prices..... 15

4.6 The eﬀects of Slant Regulation on Newspapers’ Reporting Po- sitions and Slanting Strategies...... 16

5 Implementation of other Regulatory Policies 18

5.1 Social Welfare...... 19

5.2 Price Regulation...... 21

5.3 Tax for ”Fake News”...... 23

5.4 The Average Bias level...... 24

i 6 Conclusion 26

References 31

A Appendix 32

ii Abstract

This paper examines the impact of government regulation in the media market. In a duopolistic market structure, the intervention of a state-owned media ﬁrm without bias will reduce the price of the print version of a newspaper, but will increase its digital subscription fee. Moreover, the government regulation by introducing a third public media outlet without bias will not necessarily reduce the media slanting. The User- Generated Content of a digital version of a newspaper, along with the media bias from both supply-side and the demand-side, make this kind of government regulation much less eﬀective. However, other regulatory policies such as price regulation and tax can decrease the level of slanting, especially the tax policy, which leads to an average level of slanting even less than the socially optimal level.

Keywords: Social Media, Media Bias, Spatial Model, Media Industry, Government Regulation.

1 1 Introduction

Introduction

Media industry shares many characteristics with other industries: they both have the product suppliers and consumers in the market, the quality and the price of the products are both important attributes for the consumers to make their consumption decisions, the structure of the market can also aﬀect the price and the quality of the products. . .

However, media markets are also special and different from other markets as the product that they offer, i.e. information, plays a significant role in the political and social life of their consumers ([3]). Therefore, the market failures in a media market is more important than its economic impacts. For instance, political economic studies of media market show two stylized extreme, namely, “media power” and “media capture” ([53], [8], [54]...). The former may occur when the media outlets can “control” the government by manipulate information in the elections in a democracy, while the latter implies that the government can “control” the media outlets by censorship and other ways in a dictatorial or autocratic country.

The market failure occurs in the media market when the media outlets can ﬁlter and bias information by deciding how much and which information to transmit to their consumers. This type of market failure that draws the attention of the economists is called “Media Bias” ([49]). The increasing importance of the Internet in the social life seems have ampliﬁed this market failure. Hence, the need for a more strict regulation of media bias, especially on social media, becomes more urgent in the current context.

On the one hand, the freedom of expression is crucial for the democracy; on the other hand, the full free and liberal public speech, especially on social media, is producing more and more “fake news”, “dangerous or misleading” contents, conspiracy theories...

For example, Facebook was used to provoke a surge in hate for a Mus- lim minority in Myanmar; a teenager murdered a middle-school teacher after seeing a video online, and even tweeted the victim’s head afterwards; more recently, after the riot on the U.S. Capitol of Donald Trump’s support- ers, Facebook and Twitter banned his accounts; the vast conspiracy theories about the vaccine during the COVID-19...

2 Most of the existing economic (theoretical and empirical) literature about media bias concentrates on the competition theory. Among the few economic studies about the regulatory policy applied to the media bias, they focus on mergers and competition policies. This model ﬁlls the gap of the theoretical literature of applying spatial models to the regulation of social media bias.

In this paper, I analyze the regulation of the government in a Duopolis- tic media market by introducing a third public-interest ﬁrm and by other regulation policies such as price regulation and tax policy.

This paper is organized as follows: Section2 is a brief literature review; Section3 presents the basic set-up of model with relevant deﬁnitions and hypotheses; Section4 analyzes the impact of introducing a public media outlet; Section5 explores the social welfare analysis as well as the eﬀects of other regulation policies such as price regulation and taxes; Section6 concludes.

3 2 Related Literature

As far as I know, this is the ﬁrst theoretical micro-economic model that applies the spatial model on government regulation of social media bias.

This paper contributes to the literature exploring the factors that drive the demand for media bias, see [62], [30], [55], [60], [35], [48],[46] for reviews.

This strand of literature reckons that media bias comes from the supply side or the demand side (or both) in the news market. The media slanting may result from the media companies, for example, from the bias of journalists (e.g. political or ideological bias) ([5], [56], [43],[6]...), the owners or the editors in a media ﬁrm can also impact the media slating ([20], [2], [16], [32], [33]....

Not to mention the factors outside the media ﬁrms:

The capture of the government and the politicians’ interference during the electoral campaign ([8],[55], [53], [54]...);

The interest groups such as lobbies ([5], [59], [52]);

The advertisers ([23],[9],[52],[36]) . . .

What’s more, the media market’s structure also influences the level of the media slanting, however, the effects are ambiguous. Some argue that the competition between two media firms will reduce the slanting from the media firms ([2]), while others (theoretically) prove that in a market where the consumers have heterogeneous preferences, competition between the media firms will increase the slanting level ([50]) instead.

More and more economic literature has incorporate the bias form the demand side into their models. One of the pioneering prototype models measuring the bias from the consumers, i.e. “the confirmatory bias”- a psychological concept - in the micro-economic models, is the Mullainthan and Shleifer’s work in 2005. Mullainathan and Shleifer (2005) ([50], MS 2005 hereinafter) integrate both the slanting from the media firms and the confirmatory bias from the consumers in a Hotelling model. They show that the competition in the media market will alleviate the slanting of news report if and only if the consumers are homogeneous. On the contrary, if the consumers have heterogeneous preferences for news, in order to cater to

4 this diversification of demand, the Duopolistic newspaper firms in a news market will slant even more than a Monopolist one. A series of researches are developed to study the media slants afterwards with the existence of confirmatory bias ([27],[34], [7], [39],[28], [12], [51], [44]. . . ).

However, most theoretical literature studies the impact of competition or advertising on media bias, or the multi-sided markets with a third agent such as politicians in the elections([24], [63], [13], [23],[16],[25],[27], [21], [31]...). Therefore, this paper ﬁlls the cap in the related theoretical literature.

This paper also contributes to the literature about User-Generated Content (UGC) in the social media and its impacts. UGC refers to the fact the users on social media can create content by themselves, by comments, photo and video sharing, twitters, tiktoks. . . A vast of economic literature studies the UGC on social platforms and its economic and social influence. They explores the behavioral incentives behind the UGC ([1], [22], [42]. . . ), social effects of social media in different fields from public health to elections ([10], [45],[47],[29]...), the competition and network effects ([41], [4], [37]. . . ). . .

5 3 The Model

3.1 The Newspaper Market

The payoff function of a newspaper firm depends on its revenues and the costs. The profits of a media outlet come from the subscription fees of its readers, the advertising revenues, or the political rents. Here for simplify, suppose that the newspaper firm is a profit-maximizer and its only source of revenue is the subscription fees from its readers. In terms of the costs, generally, we consider the returns to scale in the traditional print newspaper industry is increasing, that is, as the production costs (collecting data and writing the news reporting) are fixed, the variable cost equals the reprinting and delivering an additional copy ([57], [58]. . . ).

Consider a market with two private newspaper ﬁrms, each has a print version and a digital version (a web version or an application, for example). Suppose that the cost of the production (and operation) of a print version is higher than a digital one, i.e. c for the print version and δc for the digital version, with 0 ≤ δ ≤ 1 as a discount variable. Consequently, the subscription fees of a digital version of a newspaper are also lower than the print one.

A mass of consumers can subscribe either a print version or the digital version of a newspaper or both.1 The diﬀerence (besides the subscription price and the cost) between the two choices is that the consumers can interact with each other on the web or through the applications by their comments or the discussions with each other, i.e. the user-generated content (UGC hereafter). Therefore, the online users’ opinions are not only inﬂuenced by the newspapers’ news reporting but also by the UGC online.

3.2 Model Set-up

The model’s set-up is borrowed from the model of Esther Gal-or et al.’s model in 2013 ([64]) (hereinafter PET 2013) :

The role of a private newspaper ﬁrm i is to collect some data d about the state of the world t, and then to redact a piece of news n based on the data that it collects. The variable t is supposed to be normally distributed with

1That depends on whether the reader is single homing or multi-homing.

6 mean as 0 and deviation as vt, i.e. t ∼ N(0, vt), where 1/vt is the precision. The data received by a newspaper ﬁrm i is then di = t + εi, where εi is a random variable of a noise term, with εi ∼ N(0, vε)). Therefore, the data di also follows normal distribution, i.e. di ∼ N(t, vd), with vd = vt + vε.

The news reports n by a private newspaper firm i is a piece of processed information about the data received, that is, ni = di + si, where si is a slant of the newspaper i’s news reports. For simplify, suppose there are just two private newspapers firms in the market, i.e. i= {1, 2}. To distinguish the o p digital version and the print version of a newspaper, suppose that ni and ni o p are the digital and print news respectively, and si and si their slants online p p o o and offline. Hence, ni = di + si , and ni = di + si . The consumers, i.e. readers of the newspapers, are uniformly distributed between [−bo, bo]. The total number of readers is normalized to unity. A reader of type b has prior beliefs about the state of the world, and these beliefs follow normal distribution N(b, vt), that is, readers may have biased beliefs about the expected value of t. For instance, b can be the political opinions of a reader, with b ∈ [−bo, 0) is the belief of a left-wing-party supporter, b ∈ (0, bo] the belief of a right-wing-party supporter, and b=0 a neutralist’s.

As in PET 2013, we suppose that:

For a rational and unbiased reader, his/her utility from reading a private newspaper i, i= {1, 2}, is:

2 r u − χ(si) − Pi for the print version of a newspaper; U = o 2 2 (1) u − χ(si ) − Ki for the online version. For a biased reader, the bias comes from two sides:

- One called “media slant”, comes from the media’s side;

- The other is “conﬁrmatory bias”, referring to the cognitive bias of readers who prefer the news that are more consistent with their prior beliefs. Suppose that both kinds of bias will decrease the readers’ utility.

Therefore, the net utility function of a biased reader of belief b from reading a private newspaper i, i= {1, 2}, is:

p 2 p 2 b Ui = u − χ(si) − ϕ(ni − b) − Pi for a print newspaper; Ui = o o 2 o 2 (2) Ui = u − χ(si ) − ϕ(ni − b) − Ki for an online one.

7 Where u is the reservation price for the reader, χ > 0 represents the preference of readers for reduced slanting news reports, ϕ > 0 calibrates readers’ preference for hearing conﬁrming news, Ki and Pi are the subscription fees for a digital and print version of a newspaper i.

Bi is denoted as the reporting location of a newspaper i’s print version,for example, for a political newspaper, it represents its political stance during the elections.

ϕ And it satisﬁes the following conditions: si(di) = (χ+ϕ) (Bi − di) and o ϕ o si (di) = (χ+ϕ) (Bi −di), with si(di) the slanting strategy of a print newspaper o o and si (di) of a digital one, which implies that ni = γiBi + (1 − γi)di, ni = o ϕ 3 γiBi + (1 − γi)di, and γ = (χ+ϕ) . Assume also that newspaper 1 is located at the left of newspaper 2, i.e. B1 < B2.

o For the position of the digital version of a private newspaper i Bi = o o Bi +U[bi ], with U[bi ] the ”User-generated Content” by its online subscribers.

More precisely, assume that: (−b + ˆb ) (b + ˆb ) Bo = B + o 1 and Bo = B + o 2 (3) 1 1 2 2 2 2 That means the online position of a newspaper(e.g ”the political opinions” of a digital newspaper) is a by-product, i.e. the average value, of the position of its print version (e.g ”the political opinions” of a print newspaper) and UGC (e.g ”political opinions of its online subscribers.) 4

Accordingly, we suppose that because of the UGC, online readers’ opinions are more extreme than the subscribers to the print ones.

As E[di] = 0, var[di] = vd, by simple calculation, we have the expected prior utility of a reader of type b reading a newspaper i, i= {1, 2}:

 p ϕ2 2 χϕ 2 E[Ui ] = u − (Bi − b) − (b + vd) − Pi  (χ+ϕ) (χ+ϕ) 5 E[Ui] = (4) o ϕ2 o 2 χϕ 2  E[Ui ] = u − (χ+ϕ) (Bi − b) − (χ+ϕ) (b + vd) − Ki

3This transformation is to simplify mathematical analysis and the decision problems. 4It equals to the case when α = 1 in the paper of PET 2013. However, PET 2013 supposes that 0 < α < 1, here suppose that online readers have a higher power than the newspaper itself in deciding the online variant of its position. 5This expected utility function is taken from the work of Mullainathan and Shleifer

8 p Where E[Ui ] stands for the expected utility of a reader b from reading o the print version of newspaper i and E[Ui ] for the online one.

3.3 A Public-interest Newspaper Firm as an Instru- ment for Regulation

Firstly, we will see the government regulation of the media market by introducing a third public media outlet without slant. What distinguishes a public media outlet from a private one is that the former has no slant from the media side. To simplify, suppose that the public media outlet has no digital version. The intuition behind is also simple: the UGC will generate more bias as the online sources of news are only hard to be veriﬁed its truth.

The idea of introducing a public ﬁrm as an instrument for government regulation is not new (see [18], [19], [17],[38]. . . ). This idea has been applied to many markets, but mostly to mixed oligopoly markets recently, such as the health and education market where both public and private services exist. This may also be the case of the media market as the ownership of the news media ﬁrms can be either public or private.

LEMMA 1. Suppose that there exists a public newspaper company, who always reports the “truth” with clarity and objectivity without any slanting news reports. In the following part, the net utility function of a reader of belief b from reading a third public newspaper is noted as:

2 2 E[U3] = u − E[ϕ(d − b) ] − P3 = u − ϕ(vd + b ) − P3 (5)

(2005), LEMMA A1 in Appendix, P1043-1044. The market for news. American Economic Review, 2005, vol. 95, no 4, p. 1031-1053.

9 4 The Equilibrium Analysis of a Location- price Game

4.1 Timing of the game:

• Stage 1: The newspapers announce their positions of the print version and then their slanting strategy. The third public newspaper without slant is introduced;

• Stage 2: The prices of the print and digital versions of three newspapers are then decided;

• Stage 3: The consumers will make their subscription decisions, the newspapers publish their news, and online readers can interact online with each other via UGC (if they choose the digital versions).

This location-price game will be solved by backward induction: firstly, we find the indifferent readers in the stage 3, then we analyze the newspapers’ price strategies in stage 2, and at last, we can see the newspapers’ slanting strategies and reporting location choices.(See Figure1)

Figure 1: Timing of the game in a Duopolostic Newspaper Market.

10 Figure 2: Segmentation of the newspaper market, when a third public newspaper is introduced to a duopoly market of two private newspapers.

4.2 The Market Shares

o p p o Denote their Market Shares as (MS)1, (MS)1, (MS)3, (MS)2, (MS)2 respectively. As shown in Figure2, we have:

o ˆ • (MS)1 = [−b0, b1], is the market share for the online version of newspaper 1; p ˆ ˆ1 • (MS)1 = [b1, bind], is the market share for the print version of newspaper 1; ˆ1 ˆ2 • (MS)3 = [bind, bind], is the market share for the (print) newspaper 3; p ˆ2 ˆ • (MS)2 = [bind, b2], is the market share for the print version of newspaper 2; o ˆ • (MS)2 = [b2, b0], is the market share for the online version of newspaper 2. 6

First, we need to identify readers that are indiﬀerent between the digital ˆ version and the print versions of the two private newspapers, noted bi : By o p E[Ui ] = E[Ui ], i= {1, 2}, we have: o ˆ (Bi + Bi) (ϕ + χ) (Pi − Ki) bi = + 2 o (6) 2 2ϕ (Bi − Bi ) o 7 Substituting the Bi in equation (??) and (3) into equation (6), we can get:  √ ˆ 2B1+b0−2 ∆1 2 (ϕ+χ)  b1 = 3 , ∆1 = (b0 − B1) − 3(P1 − K1) ϕ2 ; √ (7) ˆ 2B2−b0+2 ∆2 2 (ϕ+χ)  b2 = 3 , ∆2 = (b0 + B2) − 3(P2 − K2) ϕ2 .

6As mentioned before, the online readers are supposed to be more extreme, that’s why the online market shares approach more to the two ends of the distribution line. 7 o ˆ As Bi is also a function of bi.

11 Then the entry of the third public ﬁrm will “steal” one part of the news market.

i Denote bind as readers who are indiﬀerent between the print versions of the two private newspapers and the public newspaper.

p Using E[U3] = E[Ui ], we have:

 2 ˆ1 ((B1) −vd) (P1−P3) (ϕ+χ) b = + 2 ;  ind 2B1 2B1 ϕ 2 (8) ˆ2 ((B2) −vd) (P2−P3) (ϕ+χ)  b = + 2 . ind 2B2 2B2 ϕ

4.3 The Equilibrium Price Choices

Given the locations of the indiﬀerent readers in (7) and (8), newspapers make their price choices Pi and Ki to maximize their following proﬁts functions:

ˆ ˆ1 ˆ  (b1+b0) (bind−b1)  Π1 = 2b (K1 − cδ) + 2b (P1 − c);  0 0  ˆ ˆ ˆ2 (b0−b2) (b2−bind) Π2 = (K2 − cδ) + (P2 − c); (9)  2b0 2b0  ˆ2 ˆ1  (bind−bind)  Π3 = (P3 − c). 2b0

The equilibrium print prices of the three newspapers are given by optimizing the proﬁt functions (9) with respect to Pi, and using the relationship ˆ ˆ ∂ˆbi between ∂bi and ∂bi derived from (6), and ind derived from (8), we get: ∂Pi ∂Ki ∂Pi

 2 2 ∗ ϕ (B1) B1B2 vd 2b0 1  P1 = c − (ϕ+χ) 2 + b0B1 + 6 − 3 + 3 1 1 ;  ( B − B )  1 2   2 2 P ∗ = c − ϕ (B2) − b B + B1B2 − vd + 2b0 1 ; (10) 2 (ϕ+χ) 2 0 2 6 3 3 ( 1 − 1 )  B1 B2   2  P ∗ = c − ϕ B1B2 + vd + 4b0 1 .  3 (ϕ+χ) 3 3 3 ( 1 − 1 ) B1 B2

As for the equilibrium online prices, by optimizing again the proﬁt func-

12 ∂ˆbi tions (9) with respect to Ki and by using derived from (7), we have: ∂Ki

 2 ∗ ∗ ϕ ˆ 2 2  K1 − P1 = c(δ − 1) − (ϕ+χ) (b1) − (b0) ; (11) 2  ∗ ∗ ϕ ˆ 2 2  K2 − P2 = c(δ − 1) − (ϕ+χ) (b2) − (b0) .

4.4 The Equilibrium Reporting Positions and Slanting Strategies

∗ ∗ By plugging the equilibrium prices P and K into the proﬁt functions Πi and then by optimizing the new proﬁt functions with respect to the locations Bi, we get the following:

 ˆ1 ˆ1 ∂Π1 1 ∂ˆb1 ∂bind ∂bind ∂P3  = ((K1 − cδ) − (P1 − c)) + (P1 − c)( + ) ;  B1 2b0 ∂B1 ∂B1 ∂P3 ∂B1 ˆ2 ˆ2 ∂Π2 1 ∂ˆb2 ∂bind ∂bind ∂P3  = (−(K2 − cδ) + (P2 − c)) + (P2 − c)( + ) .  B2 2b0 ∂B2 ∂B2 ∂P3 ∂B2 (12)

Taking B2 for example, ﬁnally, we get: ˆ 2 2 ˆ ! (b2) − (b0) (b2 + b0) ∗ 2 ∗ (B2 ) ∗ B1B2 vd 2b0 1 + − b0B + − + ∗ 2 1 1 (b + 3ˆb − 2B ) 2 6 3 3 ( − ∗ ) 0 2 2 B1 B2 2 1 vd b0B1 2b0(B1) B1 + ∗ 2 − ∗ 2 − ∗ ∗ 2 + ∗ = 0 4 6(B2 ) 3(B2 − B1) 3B2 (B2 − B1) 6B2 (13)

To compare the equilibrium results with those in the model of PET 2013, we need to simplify the above formulas by only considering the symmetric 8 ∗ ∗ ∗ o ∗ solutions hereinafter, that is, suppose that (−B1) = B2 = B , (−B1) = o ∗ o ∗ ˆ ∗ ˆ ∗ ˆ∗ ˆ1 ∗ ˆ2 ∗ ˆ ∗ (B2) = (B ) , (−b1) = (b2) = b , (−bind) = (bind) = (bind) , and suppose also that the costs of running a print and a digital newspaper equal to 0, which leads to the following results at equilibrium:

1) The equilibrium positions of indiﬀerent readers and the equilibrium

8The asymmetric solutions are either too complicated or may not exist at all.

13 prices are:

∗  ˆ1 ∗ ˆ2 ∗ ˆ ∗ (B +2b0−vd)  −(bind) = (bind) = (bind) = 6 ;  √  ∗  −ˆb∗ = ˆb∗ = ˆb∗ = 2B −b0+2 ∆ , ∆ = (b + B∗)2 − 3 (ˆb∗)2 − (b )2 ;  1 2 3 0 0   ∗ ∗ ∗ −ϕ2 ∗ 2 ∗ P1 = P2 = P = 3(ϕ+χ) ((B ) − 4b0B − vd); (14)  2  P ∗ = ϕ ((B∗)2 + 2b B∗ − v );  3 3(ϕ+χ) 0 d   2  ∗ ∗ ∗ ∗ ϕ ˆ∗ 2 2  P1 − K1 = P2 − K2 = (ϕ+χ) (b ) − (b0) .

2) And the equilibrium reporting position B∗ satisﬁes:

((ˆb∗)2 − (b )2)(ˆb∗ + b ) 0 0 + ˆ∗ ∗ (b0 + 3b − 2B ) ! (15) 1 7b v 2(v )2 (B∗)2 − 5b B∗ + 4(b )2 + v − 0 d − d = 0 36 0 0 d B∗ (B∗)2

LEMMA 2. To support the market segmentation in Figure2 at the symmetric equilibrium, and to guarantee a non-negative price, the following conditions need to be satisﬁed:9

ˆ∗ 2 ∗ p 2 p 2 ∗ (b ) B ∈ [−b0 + (b0) + vd, 2b0 + 4(b0) + vd] and B > (16) 2b0 Recall that the equilibrium prices without slant regulation in the model of PET 2013 are:10

 E E 2ϕ2 E  P1 = P2 = (ϕ+χ) b0B ; (17) E E E E ϕ2 ˆE ˆE E  K1 − P1 = K2 − P2 = 2(ϕ+χ) (b0 − b )(b0 + 3b − 2B )

9These are necessary but not suﬃcient conditions. 10To better compare the two equilibrium results, we only consider the symmetric scenario, with zero costs of production, and α = 1 based on the model of PET 2013.

14 4.5 The Eﬀects of Slant Regulation on Equilibrium Prices

Now we can observe the following results:

Proposition 1.

E ∗ E ∗ i). Pi > Pi , i= {1, 2}, and Pi > P3 . Regulation by introducing a third public newspaper ﬁrm without slant will reduce the equilibrium prices of the print versions of the two private newspapers.

∗ ∗ 2 ∗ ii). P3 < P when (B∗ − vd − b0B ) < 0. As for the price of the public no-slanting newspaper, it’s not necessarily lower that the two private ones.

Apparently, the new entry of the public newspaper in the media market decreases the price of the newspaper. As the three newspapers are all proﬁt- maximizers, the eﬀects of competition on equilibrium prices in a media market are similar to other markets.

However, a public newspaper may be more expensive than a private one under some conditions. The institution behind this scenario is quite simple:

i). The lack of an online version proﬁts to ﬁnance the public newspaper forces it to increase the price to make ends meets;

ii). The high “quality” of the news of the public firm, i.e. news without slanting, increases its “product differentiation”, and therefore can release some pressure from the fierce price competition.

Proposition 2.

∗ ∗ i). Ki > Pi , that is, after slant regulation, a digital version of a newspaper is more expensive than its print version.

∗ E ii). Ki > Ki , i.e. the subscription fees for digital newspapers become higher under slant regulation.

15 The slant regulation by introducing a public newspaper firm without bias has changed the composition of the price, especially that of a digital version. After the entry of a third newspaper firm, the digital subscription fee is much less effected by the position of the print version, as there is no ∗ more ”B ” in the (Pi − Ki) of (14) compared with that in (17).

This result corresponds to the assumption that the Internet (UGC) has a higher power than the newspaper itself in deciding the online variant of its position at the beginning of this paper. 11 Once the UGC has a higher discretion in deciding the position of a digital newspaper, it’s no longer a by-product of its print version, but more like a new diﬀerentiated product.

It may be due to a “Daily-me” effect ([61], [51]. . . ), where UGC helps every user online find information that is more consistent with his/her prior beliefs or even news reports that cater to his/her beliefs, especially for the extremists who can hardly to get approved in their ”offline” life. Therefore, for this segmentation of consumers, they are willing to pay higher prices to digital newspapers.

This also corresponds to the characteristics of UGC : for an online newspaper and its online readers, they try to get higher proﬁts not only by com- peting on prices, but also by drawing “attention” of consumers ([11],[15], [26], [14]. . . ). For example, the more an article is transferred online and is clicked by online readers, the more it becomes popular and get more readers, no matter how credible it is. 12

4.6 The eﬀects of Slant Regulation on Newspapers’ Reporting Positions and Slanting Strategies

In terms of the reporting positions and the slanting strategies at equilibrium. We can see that it’s hard to ﬁnd a simple and direct solution. However, we can at least rule out some hypotheses and still draw some interesting conclusions.

11See footnote 4 in section3. 12Sometimes the “Fake News” can get much more attention than the true news, as the former always has a more “eye-catching” title and more astonishing contents.

16 Rewrite the (15) as two parts:

((ˆb∗)2 − (b )2)(ˆb∗ + b ) (A) = 0 0 ˆ∗ ∗ (b0 + 3b − 2B ) ! (18) 1 7b v 2(v )2 (B) = (B∗)2 − 5b B∗ + 4(b )2 + v − 0 d − d 36 0 0 d B∗ (B∗)2

LEMMA 3.

i) As for the former part (A):

( 3(ˆb∗+b ) (A) > 0 when B∗ > 2 0 ; 2 (19) (A) ≤ 0 otherwise. ii) Solutions for the second part of (B) = 0 are (see Figure3): √ √  2 2  B = b0− (b0) −8vd ,B = b0+ (b0) −8vd , 1 2 2 2 (20) p 2 p 2  B3 = 2b0 − 4(b0) + vd,B4 = 2b0 + 4(b0) + vd.

∗ iii) The conditions satisfying the symmetric assumptions, i.e. (−B1) = ∗ ∗ 2 B2 = B ,B1 < B2, vd = δd > 0, are:

p 2 p 2 p 2 (2b0 − 4(b0) + vd) < 0 < (−b0 + (b0) + vd) < (2b0 + 4(b0) + vd) (21)

Combined with the conditions in LEMMA 2, we can draw the following conclusions:

Proposition 3.

∗ 2 2 i) When (b2) > 3 b0, there exists an equilibrium reporting position for the private newspapers denoted as B∗, taking the newspaper 2 for example, satisfying the conditions in equation (15) and the conditions in LEMMA 2.

ii) And this equilibrium reporting position is more extreme than when there are only print newspapers in the news market in the model of MS ∗ 3 2005, i.e. B > 2 b0. Hence, it’s also more extreme than the equilibrium level without slant regulation (BE) in the model of PET 2013.

Under slanting regulation, the equilibrium slanting level of the (private) newspapers may be higher than the one without slanting regulation. The two

17 Figure 3: The ranges of possible values of the equilibrium reporting position of newspaper 2.

private newspapers may oﬀer more extreme news when a public unbiased newspaper is introduced compared to the scenario when there is no slant regulation in the newspaper market (PET 2013) or the case when there is only print versions of newspapers in the news market (MS 2005).

As we can see from the Figure3, the equilibrium slanting level increases with the value of Vd and bo, i.e. the variance of the date and the extremist opinions of its readers. The more variant data the newspapers collect, the more exogenous readers are, the government regulation by introducing a public newspaper without bias has less eﬀect on reducing the slanting level of the private newspapers.

5 Implementation of other Regulatory Poli- cies

We have shown that the government regulation of a Duopolistic newspaper market by introducing a third public newspaper without slant is not as ef- fective as we thought. Now we turn to other alternative regulatory policies such as price regulation and tax policy, to examine their eﬀects on reducing the media bias.

We will return to the original model of PET 2013 in the following anal-

18 Figure 4: Segmentation of the newspaper market in the model of PET 2013.

yses (see Figure4), but to simplify, we still assume that the costs are zero.

5.1 Social Welfare

LEMMA 4. Deﬁne the social welfare of the Duopolistic market in PET 2013 as the total surplus of the newspaper ﬁrms and their readers:

ˆ ˆ Z b1 0 Z bind p Z b2 p Z b0 0 U1 U1 U2 U2 SW = db + db + db + db + Π1 + Π2 ˆ −b0 2b0 b1 2b0 bind 2b0 b2 2b0  ˆb b  2 R 1 o 2 R ind 2 3 1 ϕ (B1 − b) db + ˆ (B1 − b) db+ 2χϕ (b ) = u − −b0 b1 − 0 + v b  ˆ  d 0 2b0 (ϕ + χ) R b2 2 R b0 o 2 (ϕ + χ) 3 (B2 − b) db + (B − b) db bind b2 2 (22)

Optimizing the above equation with respect to the (print and digital) reporting locations of newspaper i separately, we get:

 ˆ ˆ 0 (b1−b0 (bind+b1)  B = ); B1 = ; i 2 2 (23) ˆ ˆ (bind+b2) 0 (b1−b0  B2 = 2 ; Bi = 2 )

As shown in Figure5 and Figure6, The socially optimal slanting is the mean value of the opinions of readers in the print or digital market.

However, the optimal (ﬁrst-best) reporting locations can be diﬀerent according the value of α.

1) Scenario 1: When 0 < α < 1, i.e. the online variant of the online news reports are not totally decided by UGC, we get:

19 Figure 5: The optimal (ﬁrst-best) reporting location choices with 0 < α < 1.

Figure 6: The symmetric solutions for optimal (ﬁrst-best) reporting location choices (0 < α < 1).

Proposition 4. As shown in Figure5 and Figure6, in the original model of PET 2013:

i) The symmetric solutions for optimal (ﬁrst-best) reporting locations ˆ ˆ 0 0 (−b−b0) −ˆb ˆb (b+b0) ˆ ˆ ˆ are : (B1 ,B1,B2,B2 ) = 2 , 2 , 2 , 2 , with (−b1) = b2 = b.

ii) And the optimal level of slants is:

0 0 SW (s1(d1), s1(d1), s2(d2), s2(d2)) = ! −ϕ −ϕ ˆb ϕ ˆb ϕ (ˆb + b ) (ˆb + b + d ), ( + d ), ( − d ), ( 0 − d ) . (ϕ + χ) 0 1 (ϕ + χ) 2 1 (ϕ + χ) 2 2 (ϕ + χ) 2 2

2) Scenario 2: When α = 1, i.e. UGC’s eﬀect on the online news reports attends to its maximal level, we can observe that:

Proposition 5.

i) The symmetric solutions for the optimal (ﬁrst-best) reporting loca- 0 0 −b0 b0 tions are: (B1 ,B1,B2,B2 ) = ( 2 , 0, 0, 2 );

20 ii) And the optimal level of slants in this scenario is:

0 0 SW (s1(d1), s1(d1), s2(d2), s2(d2)) = −ϕ b −ϕd −ϕd ϕ b ( 0 + d ), 1 , 2 , ( 0 − d ) . (ϕ + χ) 2 1 (ϕ + χ) (ϕ + χ) (ϕ + χ) 2 2

iii) The socially optimal payoﬀs for the two private newspaper ﬁrms are: SW K1 K2 (Π1, Π2) = ( 2 , 2 ). Under the assumption of α = 1, that is, when the UGC plays a more important role than the newspaper itself in deciding the reporting position of its digital version,e.g. left or right in the election, when social welfare is maximized, the news market is totally occupied by the social media (the digital versions of the two newspapers). The “traditional” print newspapers are “crowed out” of the market by the social media.

The optimal reporting locations for the two digital versions of newspaper are the same. The socially optimal reporting strategy corresponds to the “Minimum Diﬀerentiation Principle” in Hotelling’s model ([40]).

Moreover, the optimal slanting level for a traditional print newspaper depends on the data it collects ( di), the degree of its readers’ preference for conﬁrming news (ϕ) and their dislike for slanting news (χ).

The social welfare is maximized when the social media expresses more diverse but less extreme opinions. The optimal slanting level for a digital newspaper depends not only on its data source (di), on its readers’ preference for conﬁrming news (ϕ) and dislike for slanting news (χ), but also on the 13 extremist readers’ opinions (b0).

5.2 Price Regulation

We now turn to an other regulation policy, i.e.price regulation, and see its eﬀects on decreasing the level of slanting.

Suppose that government sets a unique price P for the print newspapers and K for the digital versions, and again, we only see the symmetric solutions

13That is also due to the assumption that the UGC’s eﬀect attends to its maximal level, i.e. α = 1.

21 when the costs are 0. The new payoﬀ functions for the two private newspapers are:  ˆ ˆ (b1+b0) (bind−b1)P P b0 ˆb1 Π1 = K + = (bind + − );  2b0 2b0 2b0 2 2   ˆ ˆ (b0−b2) (b2−bind) P b0 ˆb2 Π2 = K + P = (−bind + + );  2b0 2b0 2b0 2 2   P = 2K. By simple calculations, we observe that:

∂Π1 ∂Π2 ∂Π1 ∂Π2 > 0, < 0, 0 < 0, 0 > 0. B1 B2 B1 B2

Therefore we can get the following results:

Proposition 6. Under price regulation: 0 0 i) The equilibrium reporting positions are (B1, B1, B2, B2) = (−b0, 0, 0, b0); ii) The slanting strategies are: −ϕ −ϕd −ϕd ϕ (s0(d ), s (d ), s (d ), s0(d )) = (b + d ), 1 , 2 , (b − d ) . 1 1 1 1 2 2 2 2 (ϕ + χ) 0 1 (ϕ + χ) (ϕ + χ) (ϕ + χ) 0 2 iii) When regulated price of the print newspapers is twice that of the digital versions, i.e.when P = 2K, the two newspapers can maximize their proﬁts, which are:  P (b0−ˆb1) 3 (ϕ+χ) 2 Π1 = = P − 2 2 (P ) ;  2b0 2 4 8(b0 )ϕ

P (b0+ˆb2) 1 (ϕ+χ) 2  Π2 = = P − 2 2 (P ) . 2b0 2 2 8(b0 )ϕ We can see from the above functions that the only possibility to guarantee the non-negative payoﬀs for the two private newspapers are when P = 2K = 0. Therefore, under price regulation, the two private newspapers get 0 proﬁts at the equilibrium.

Compared to the social optimal situation, the price regulation has de- creased the slanting level of a print newspaper, while the slant level of the digital versions augments compared to the socially optimal slanting level.

The market share for print newspapers decreases to zero, i.e. the news market is totally occupied by the social media and the traditional print newspapers are ”crowed out”. As the regulated prices for the two kinds of newspapers are all 0, there is no longer any proﬁt to publish a print newspaper. However, under the assumption of zero costs, the online newspapers still exist.

22 This may be due to the ”competition for attention” effect ([11],[15], [26],[14]. . . ). Even when there is no longer pecuniary motivation to publish a print newspaper, a digital newspaper can still draw the attention of readers, make them interact with each other, generate online content (UGC), and may therefore gain reputation (well, good or bad...) for the newspaper firms. In this case, the culture, social and political significations of a newspaper for their readers are much more important than its economic contributions to the society.

5.3 Tax for ”Fake News”

Consider the government will impose a tax for “Fake News”, named T. The payoﬀs of the two private newspapers then turn to: ˆ ˆ (b1 + b0)K (bind − b1)P 2 0 2 Π1 = + − T [Ed(s1(d1) ) + Ed(sd (d1) )] 2b0 2b0 ˆ ˆ 2 (b1 + b0)K (bind − b1)P T ϕ 2 0 2 = + − 2 (B1) + (B1 ) ; 2b0 2b0 (ϕ + χ) ˆ ˆ 2 (b0 − b2)K (b2 − bind)P T ϕ 2 0 2 Π2 = + − 2 (B2) + (B2 ) . 2b0 2b0 (ϕ + χ)

Optimizing the payoff functions with respect to Pi, we can get the same results in the model of PET 2013.14 Then replace the equilibrium prices into the payoff function, and optimize the news payoff functions with respect to Bi, we can draw the following conclusions:

Proposition 7. Under tax regulation:

i) The equilibrium reporting positions are: ˆ 2 2 (b) + (b0) T T T −(B1) = (B2) = B = 1 ; b0(4T + 3 ) ˆ 2 2 (b) + (b0) ˆ 0 T 0 T 0 T (b0 + b) −(B1 ) = (B2 ) = (B ) = 1 + . b0(4T + 3 ) 2 14See the equation (11) in the model of PET 2013, Yildirim, Gal-Or, and Geylani: User-Generated Content and Bias in News Media, Management Science 59(12), pp.2660.

23 The equilibrium reporting positions of the newspapers (print and digital versions) get extreme when the tax level for slanting increases.

ii) The prices at equilibrium are: ˆ 2 2 2 2 (b) + (b0) T T T ϕ ϕ P1 = P2 = P = 2b0B = 1 ; (ϕ + χ) (ϕ + χ) (2T + 6 )  ˆ 2 2 ˆ  2 ˆ ˆ 3 (b) + (b0) (b + b0) T T T ϕ (b0 + 3b)(b0 − b) K1 = K2 = K =  +  . (ϕ + χ) 2 b0(12T + 1)

The equilibrium (print and digital) prices of the newspapers increases with the level of slanting but decreases with tax level (that is so wired).

5.4 The Average Bias level

Deﬁne the average bias level (ARB) for the heterogeneous readers as: Z 2 ARB = Ed[(ni − di) ] = b 2 ϕ ˆ 0 2 ˆ 2 ˆ 2 ˆ 0 2 2 (b1 + b0)(B1 ) + (bind − b1)(B1) + (b2 − bind)(B2) + (b0 − b2)(B2 ) 2b0(ϕ + χ) We can then compare the average bias level under the above three diﬀerent regulation policies: 15

15Again, we only see the symmetric solutions for analytic and mathematical reasons.

24 2 2 ˆ SW ϕ ˆ ˆ (Symmetric Solutions) ϕ b0(b0 − b) (ARB) = 2 b0(b1−b2+2b0) =−−−−−−−−−−−−→ 2 ; 8(ϕ + χ) (−ˆb1=ˆb2=ˆb) (ϕ + χ) 4 2 2 PR ϕ ˆ ˆ (Symmetric Solutions) ϕ ˆ (ARB) = 2 b0(b1−b2+2b0) =−−−−−−−−−−−−→ 2 b0(b0−b); 2(ϕ + χ) (−ˆb1=ˆb2=ˆb) (ϕ + χ)   2 ˆ 2 ˆ 2  2 2(b0) − (b1) − (b2) T ϕ  T 2 T (ARB) = 2 (B ) +   B + (ϕ + χ)  2b0 ˆ ˆ 2 ˆ ˆ 2 (b1 + b0)(b1 − b0) + (b0 − b2)(b0 + b2)

8b0 (Symmetric Solutions) −−−−−−−−−−−−→ (−ˆb1=ˆb2=ˆb)   2 ˆ 2   2 ˆ 2 2 (b0) − (b) ˆ ˆ 2 3 (b0) + (b) ϕ  T 2 T (b0 − b)(b0 + b)  T = 2 (B ) +   B + ,B = . (ϕ + χ)  b0 4b0  12T + 1

And when ˆb = 0, we further have:

 ϕ2 (b )2 (ARB)SW = 0 ;  (ϕ+χ)2 4   PR ϕ2 2 (ARB) = (ϕ+χ)2 (b0) ;  2 2 2  T ϕ T 2 T (b0) T 3(b0)  (ARB) = (ϕ+χ)2 (B ) + b0B + 4 ,B = 12T +1 .

Proposition 8. (ARB)PR > (ARB)SW > (ARB)T .

The average bias under tax regulation is even smaller than the socially optimal average bias. The average bias level under the price regulation is the highest.

25 6 Conclusion

This paper analyzes the eﬀects of government regulation on social media market.

In a Duopolistic newspaper market, two newspapers offer two versions of their products - a print one and a digital one. The latter is different from the former version of newspaper as online readers can generate content themselves by interacting with each other. The User-generated content has a non-negligible effect on deciding the positions of a newspaper’s online version. Sometimes, UGC is one of the most important reasons for people spreading Fakes News and extremists opinions on the social media.

Introduction of a third public ﬁrm without slant seems to be a feasible solution to resolve the growing media bias in news reports, especially on the social media. However, this paper shows that when media bias comes from both supply and demand side, even the government regulation fails to weaken the power of UGC on the social media. Compared to the market without slant regulation, the only positive eﬀect is that the regulation reduces the subscription fee of a print newspaper. On the contrary, the subscription fee of a digital newspaper increases, and the slanting level may get higher under some conditions.

In terms of other regulation policies, compared to the socially optimal level of slanting:

• The price regulation decreases the level of slanting of a print newspaper, but increase the online slanting level;

• Under tax regulation, the slanting level (both print and digital ones) decreases with the tax level;

• What’s more, the average bias under tax is smaller than the socially optimal average bias, and the average bias under the price regulation is the highest.

26 References

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31 A Appendix