Content Provision in the Media Market with Single-Homing and Multi-Homing Consumers

Armando J. Garcia Pires

doi:10.1515/rne-2020-0021

Article

Content Provision in the Media Market with Single-Homing and Multi-Homing Consumers

Armando J. Garcia Pires

Published/Copyright: October 5, 2020

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From the journal Review of Network Economics Volume 19 Issue 1

Abstract

In this paper, we analyze the effects on content provision in the news market of single-homing (i.e. when readers consume news from just one outlet) and multi-homing (i.e. when readers can choose to consume news from competing outlets). Media firms compete on content provision and on advertising revenues. Readers have an ideal variety of content and experience a disutility from consuming news that differs from their ideal variety. In addition, readers have a preference for single-homing and for multi-homing. In this set-up, we show that media firms only diversify content with single-homing, but not with multi-homing. The reason for this is that competition for readers and advertising is lower under multi-homing than under single-homing, since multi-homing readers consume from all media outlets. We derive the consequences of single-homing and multi-homing for profits, consumer surplus and social welfare. We also discuss the implications of our results for the current debate in the media market related with social media and echo chambers.

Keywords: social media; echo chambers; content provision; two-sided markets; multi-homing

JEL Classification: D43; L13; L82; L86

Corresponding author: Armando J. Garcia Pires, Centre for Applied Research at NHH (SNF), Helleveien 30, 5045 Bergen, Norway, E-mail: armando.pires@snf.no

A. Appendix

Single-Homing: FOCs

FOCs for advertising:

(34)dΠidai=t(di−dj+1)(α−2ai)+ηai(3ai−2aj)−αη(2ai−aj)2t, i,j=1,2 with i≠j.

FOCs for content:

(35)dΠiddi=−t(di−dj+3)(t(di−dj+3)−2αη)+18γη2di18η2, i,j=1,2 with i≠j .

Single-Homing: SOCs

SOCs for advertising:

(36)d2Πidai2=−αη+t(di−dj+1)−η(3ai−aj)t<0, i,j=1,2.

We can see that at the symmetric equilibrium the SOC simplifies to:

(37)d2Πidai2=−αη+t−2ηait<0, i=j=1,2 .

The SOC is satisfied if α>2ηai−tη, i = j = 1, 2. Since ai=tη, then the SOC is satisfied if α>tη.

SOCs for content:

(38)d2Πiddi2=−t2(di−dj+3)−η(tα−9γη)9η2<0, i,j=1 ,2 .

At the symmetric equilibrium, the SOC equals:

(39)d2Πiddi2=−3t2−η(tα−9γη)9η2<0, i=j=1,2 .

The SOC is satisfied if α<3t2+9γη2ηt. As a result the game is valid for tη<α<3t2+9γη2ηt. The SOCs in the single homing case then say that the advertising market cannot be too big or too small. The intuition is the following. Since firms derive all the revenues from advertising, if the advertising market is too small, firms cannot make positive profits, and as a result, all firms exit the market. If the advertising market is too big, and since under the single homing case firms diversify content, this means that it is possible that content diversification can either be bigger than the line and/or that the content provision segments of the two firms overlap. Since under single homing consumers only consume one variety, overlap of content is not possible in equilibrium.

Multi-Homing: FOCs

FOCs for advertising:

(40)dΠidai=((VM−VS)+tdi)(α−2ai)−ηai(2α−3ai)t, i,j=1,2 .

FOCs for content:

(41)dΠiddi=−γdi+α2(VM−VS+tdi)((4α3η3+(VM−VS)(13α2η2+2(VM−VS)(4αη+(VM−VS))))8(αη+(VM−VS)+tdi)4+(tdi(13α2η2+2tdi(4αη+tdi)+2(VM−VS)(8αη+3(VM−VS)+3tdi)))8(αη+(VM−VS)+tdi)4), i,j=1,2 .

Multi-Homing: SOCs

SOCs for advertising:

(42)d2Πidai2=−2αη+(VM−VS+td1−3ηa1)t, i=1,2 .

Substituting for ai=α(VM−VS)2(αη+(VM−VS)) and d_i = 0, we obtain:

(43)d2Πidai2=−(VM−VS)(2(VM−VS)+αη)+2α2η2((VM−VS)+αη)t<0, i=1,2 .

Then the SOC is always satisfied since (V_M − V_S) > 0.

SOCs for content:

(44)d2Π1dd12=−tα4η2(VM−VS)((VM−VS)−7αη+2tdi)−2α2η2−tdi(7αη−tdi)4(αη+(VM−VS)+tdi)5−γ<0, i=1,2 .

Substituting for d_i = 0, we obtain:

(45)d2Π1dd12=−tα4η2(VM−VS)((VM−VS)−7αη)−2α2η24(αη+(VM−VS))5−γ<0, i=1,2 .

The SOCs for content is satisfied if γ>−tα4η2(VM−VS)((VM−VS)−7αη)−2α2η24(αη+(VM−VS))5. We can see that the numerator has two solutions in relation to (V_M − V_S): αη(7+57)2>0 and αη(7−57)2<0. Furthermore, the numerator is convex in (V_M − V_S). As such the numerator is always positive for (VM−VS)>αη(7+57)2>0 and for (VM−VS)<αη(7−57)2<0. When this occurs, we have that −tα4η2(VM−VS)((VM−VS)−7αη)−2α2η24(αη+(VM−VS))5<0 and the SOC is as a result satisfied, since γ > 0.

Note that if (VM−VS)<αη(7−57)2<0, multi-homing does not arise in equilibrium (see Eq. (21)). In other words, we fall back in the single-homing case, and therefore there are no differences between the single-homing and the multi-homing case. Since we are interested in comparing what happens in a media market where readers single-home and where readers multi-home, we look at the case where (VM−VS)>αη(7+57)2>0.

In the multi-homing case, the SOC then only demands that consumers have a higher preference for multi-homing than single-homing. If the SOC is not satisfied, we follow back in the single homing case.

Alternative Utilities: Consumers Care About the Size of the Line Segment of Content Provided by Media Firms

In the model in the paper consumers care about their ideal variety. We could what ask what would occur if they also care about the size of the line segment of content provided by media firms. There are potentially several ways to do this. In here, we consider two alternatives.

In the first, individual utility from consuming news is just multiplied by the size of the content provision segment provided by each firm, i.e. in the single-homing case V_Sd_i; and in the multi-homing case V_Md_i, with i = 1,2.

In this case, under single-homing, the utility of a reader who only consumes from media firm 1 and is located outside the multi-content segment of media firm 1, is:

(46)US=VSd1−t(x−d1)−ηa1 ,

and under multi-homing, the utility of a reader, located outside the multi-content segments of the two media firms and who consumes from both media firms is:

(47)UM=VMd1−t((x−d1)+(1−x−d2))−η(a1+a2) ,

In the second case, we consider that consumers care about the difference in content provision provided by each firm, i.e. (d₁ − d₂) for a consumer in the left segment and (d₂ − d₁) for a consumer in the right segment.

In this case, under single-homing, the utility of a reader who only consumes from media firm 1 and is located outside the multi-content segment of media firm 1, is:

(48)US=VS−t(x−d1)−ηa1+(d1−d2) ,

And under multi-homing, the utility of a reader, located outside the multi-content segments of the two media firms and who consumes from both media firms is:

(49)UM=VM−t((x−d1)+(1−x−d2))−η(a1+a2)+(d1−d2) ,

It can be easily be seen that since media firms are symmetric, in both cases, we get the same indifferent consumer as in the main model. Therefore, our results in the main text are not changed.

Numerical Simulations (An Example)

If we set η = 0.3; γ = 1; and t = 1, we have from Eq. (32) that 150 < α < 452. 7. As a result, for 150=tη<α<225=3t2δ, media firms do not diversify content; and for 225=3t2δ<α<452.7, media firms diversify content. We then make simulations for parameter values under these two intervals. Setting for instance α = 400, which represents a large add market and that media firms diversify content under single-homing, from Eq. (33), we must have that VM−VS>4(57+7)3. We then plot Eqs. (50)–(55) in the interval VM−VS>4(57+7)3.

We proceed in the same way with different values of the parameters, to check for high and low η, for high and low γ; for high and low t, and for high and low α.

Note that since we plot Eqs. (50)–(55) in the V_M − V_S, we do not need to do simulations for high and low values of V_M − V_S, since this can be seen from the figures.

Difference in Profits, Consumer Surplus and Social Welfare: Single-Homing Versus Multi-Homing

Start with the scenario where α<3t2δ (small advertising market, media firms do not diversify content in both the single-homing and the multi-homing cases). The difference in profits between the single-homing case and the multi-homing case is:

(50)ΠSH−ΠMH=(αδ−t)tδ2−(2(VM−VS)+αδ)((VM−VS)+2αδ)(VM−VS)2α24((VM−VS)+αδ)3t, if α<3t2δ .

The difference in consumer surplus between the single-homing case and the multi-homing case is:

(51)CSSH−CSMH=VS−5t4−(VM−VS)2(2(VM−VS)+αδ)2−2t(VM−2VS)(αδ+(VM−VS))22((VM−VS)+αδ)2t+(αδ+2(VM−VS))3(VM−VS)312((VM−VS)+αδ)3t2, if α<3t2δ .

The difference in social welfare between the single-homing case and the multi-homing case is:

(52)WSH−WMH=VS+(δ(4α−5δ)−4t)t4δ2−(VM−VS)2(2(VM−VS)+αδ)2−2t(VM−2VS)(αδ+(VM−VS))22((VM−VS)+αδ)2t−(δα2(6tα−δ(VM−VS))−(VM−VS)(4(VM−VS)((VM−VS)+αδ)−3tα2))12((VM−VS)+αδ)3t2(2(VM−VS)+αδ)−1(VM−VS)−2, if α<3t2δ .

Turn now to the case with α>3t2δ (large advertising market, media firms diversify content in the single-homing case, but not diversify content in the multi-homing case). The difference between profits in the single-homing and the multi-homing scenario equals:

(53)ΠSH−ΠMH=(4δ2α(9γδ−tα)−3t(3t2+4δ(3γδ−tα)))t36δ4γ−(2(VM−VS)+αδ)((VM−VS)+2αδ)(VM−VS)2α24((VM−VS)+αδ)3t, if α>3t2δ .

The difference in consumer surplus between the single-homing and the multi-homing scenario is:

(54)CSSH−CSMH=VS−3t2(t(3t−4αδ)+6γδ2)+δ2(4αt(tα−3γδ)+45γ2δ2)36δ4γ2−(VM−VS)2(2(VM−VS)+αδ)2−2t(VM−2VS)(αδ+(VM−VS))22((VM−VS)+αδ)2t+(αδ+2(VM−VS))3(VM−VS)312((VM−VS)+αδ)3t2, if α>3t2δ .

With respect to social welfare, we have:

(55)WSH−WMH=VS+3t2(t(4αδ−3t)(γ+1)−6δ2γ(2γ+1))+δ2(4αt(3δγ(3γ+1)−αt(γ+1))−45γ2δ2)36δ4γ2−(VM−VS)2(2(VM−VS)+αδ)2−2t(VM−2VS)(αδ+(VM−VS))22((VM−VS)+αδ)2t−(δα2(6tα−δ(VM−VS))−(VM−VS)(4(VM−VS)((VM−VS)+αδ)−3tα2))12((VM−VS)+αδ)3t2(2(VM−VS)+αδ)−1(VM−VS)−2, if α>3t2δ .

Type of Content Provided by Media Firms

In this paper, our aim is to look at content competition with single-homing and multi-homing consumers. Our aim is to focus in different type of content provided in media markets. Below, we give some examples of content that can be considered in the context of our model.

Competition between local media outlets. Consider two local newspapers of two different cities (city 1 and city 2) but possible nearby cities (but not necessarily). Media outlet 1 is located on the left at point zero and media outlet 2 on the right at point one. Consumer located closer to point 0 like news about city 1, consumers located closer to point 1 like news about city 2 and consumers in between like a mix of news about city 1 and 2. What our model says is that under single-homing, local media outlet 1 will provide mostly news about city 1 but also a mix of news from both city 1 and 2 in order to attract consumers that like a mix of news from both cities and to not lose them to media outlet 2. Under multi-homing, media outlet 1 will just provide news about city 1. The reason is that consumers that like also of news of city 2 can just go to newspaper 2 and consume news from media outlet 2, and media outlet 1 will not lose them since they will continue to consume from media outlet 1.

Competition between national and local media outlets. Consider a national newspaper and a local newspaper. Media outlet 1 is the national outlet and is located on the left at point zero. Media outlet 2 is the local outlet and is located on the right at point one. Consumer located closer point 0 like national news, consumers located closer to point 1 like local news, and consumers in between like a mix of national and local news. What our model says is that under single-homing, the national media outlet will provide mostly national news but also a mix of local and national news in order to attract consumers that like a mix of local and national news and not lose them to media outlet 2. Under multi-homing, the national media outlet will just provide national news. The reason again is that consumers that like a mix of local and national news can just go to the local newspaper and consume local news, and the national media outlet will not lose them since they will continue to consume from national outlet. A similar reasoning can be applied to the local newspaper.

Competition between generalist media outlets and specialist media outlets (like sports media outlets). Media outlet 1 is the generalist outlet and is located on the left at point zero. Media outlet 2 is the specialist outlet and is located on the right at point one. Consumer located closer point 0 like generalist news, consumers located closer to point 1 like specialist news, and consumers in between like a mix of specialist and generalist news. What our model says is that under single-homing, the generalist media outlet will provide generalist news but also a mix of generalist and specialist news in order to attract consumers that like a mix of generalist and specialist news and not lose them to media outlet 2. Under multi-homing, the generalist media outlet will just provide generalist news. The reason again is that consumers that like a mix of generalist and specialist news can just go to the specialist newspaper and consume specialist news, and the generalist media outlet will not lose them since they will continue to consume from the generalist outlet. A similar reasoning can be applied to the specialist newspaper.^[24]

Competition between generalist media outlets. Consider two generalist media outlets that compete for political news (left wing versus right wing). Media outlet 1 is the left outlet and is located on the left at point zero. Media outlet 2 is the right outlet and is located on the right at point one. Consumer located closer point zero like left news, consumers located closer to point one like right news, and consumers in between like a mix of left and right news. What our model says is that under single-homing, the left media outlet will provide left news but also a mix of left and left-to-the-center news in order to attract consumers that are closer to the center. Under multi-homing, the left media outlet will just provide left news. The reason again is that consumers that like a mix of left and right news can just go to the right newspaper and consume right wing news, and the left media outlet will not lose them since they will continue to consume from the left wing media outlet. A similar reasoning can be applied to the right newspaper.

Competition between specialist media outlets. Consider two specialist media outlets that covers for instance just sport news (for instance car races and football). Media outlet 1 is the football outlet and is located on the left at point zero. Media outlet 2 is the car races outlet and is located on the right at point one. Consumer located closer point zero like football news, consumers located closer to point one like car race news, and consumers in between like a mix of football and car races news. What our model says is that under single-homing, the football media outlet will provide football news but also a mix of football and car races news in order to attract consumers that like also car races. Under multi-homing, the left media outlet will just provide football news. The reason again is that consumers that like a mix of football and car races news can just go to the car races newspaper and consume car races news, and the football media outlet will not lose them since they will continue to consume from the football media outlet. A similar reasoning can be applied to the car race newspaper.

Acknowledgment

The author would like to thank the editor Lukasz Grzybowski, and two anonymous referees for extremely helpful comments and suggestions.

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Received: 2020-03-30

Accepted: 2020-09-15

Published Online: 2020-10-05

Published in Print: 2020-03-26

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Articles in the same Issue

https://doi.org/10.1515/rne-2020-0021

Keywords for this article

social media; echo chambers; content provision; two-sided markets; multi-homing