Strategic Complementarities in a Model of Commercial Media Bias

Abstract

Media content is an important privately supplied public good. While it has been shown that contributions to a public good crowd out other contributions in many cases, the issue has not been thoroughly studied for media markets yet. We show that in a standard model of commercial media bias, qualities of media content are strategic complements, whereby investments into quality can crowd in further investments and engage competitors in a race to the top. Therefore, financially strong public service media can mitigate commercial media bias: the content of commercial media can be more in line with the preferences of the audience and less advertiser-friendly in a dual (mixed public and commercial) media system than in a purely commercial media market.

1. Introduction

Media content belongs to the most important cases of privately supplied public goods. Its consumption is non-rival, and in many cases like free TV or freely available Internet content no exclusion is taking place. Media content differs markedly from other public goods, though, because media outlets typically rely on advertising revenues instead of charging their consumers a pecuniary price. The economic analysis of the private supply of media content as a public good must take this multi-sided nature of media markets into account (Anderson & Coate, 2005). Recent literature has made major progress in this research area (see Anderson & Jullien, 2015; Jullien et al., 2021).

One important result from the theory of private public good supply is that, under fairly general conditions, private contributions to a public good are strategic substitutes, i.e., higher private contributions to the public good are crowding out other private contributions (for overviews, see Chapter 6 of (Batina & Ihori, 2005), and Finding F9 in (Buchholz & Sandler, 2021)). Surprisingly, this issue has not been thoroughly examined for media markets, even though it is highly relevant for the welfare analysis of media policy. E.g., in discussions about the proper role and scope of public service media (PSM), one crucial question is whether raising the quality of a regulated PSM will increase or decrease the quality of its commercial—i.e., profit-maximizing—competitors.

There are two conflicting views. On the one hand, PSM could crowd out private investment and innovation in media markets. E.g., the existence of PSM may lead to less entry of commercial media; see (Berry & Waldfogel, 1999) for empirical evidence. Similarly, (Armstrong & Weeds, 2007a) show that in a duopoly where a PSM and a commercial broadcaster compete, raising the quality of PSM partially crowds out the commercial broadcaster and lowers its quality. This reasoning is echoed by regulation authorities like Ofcom (2004) in the UK and the Scientific Advisory Board at the Federal Ministry of Finance in Germany (Wissenschaftlicher Beirat beim Bundesministerium der Finanzen, 2014).

However, PSM might also foster a “competition for quality”, whereby public and commercial media compete for audiences. This reasoning goes back to (Coase, 1947), pondering that PSM might induce a “natural rivalry to furnish the most attractive programs” (p. 197). Indeed, recent empirical evidence suggests that in countries where PSM invest into high-quality media content, the quality of commercial media tends to be high, too (Simon, 2013). Similarly, (Sehl et al., 2020) find that, controlling for GDP, per capita revenues of PSM and commercial broadcasters are positively correlated across EU countries. These correlations are in line with a crowding in effect of PSM, i.e., the presence of strong PSM coincides with flourishing commercial media.1

In this paper, we show that in a model of commercial media bias, program qualities in terms of unbiased reporting are strategic complements rather than strategic substitutes.2 Unbiased reporting here refers to a program that fully and truthfully reports facts as opposed to withholding information. E.g., advertisers might prefer the media to hide unfavorable facts about their products; prime examples include the tobacco and carbon-emitting industries. Viewers prefer high program quality, while advertisers prefer the opposite. The strategic complementarity stems from the media’s fundamental trade-off in these models: Raising program quality increases the value of the program for the audience but decreases the willingness to pay of the advertisers to reach consumers.3 The latter effect becomes less important when a media company has a smaller audience; hence, its incentives to raise program quality are higher. Thus, in a media market with both PSM and commercial media, raising the PSMs’ program quality reduces the commercial media’s audiences and thereby also their implicit cost of increasing their own program quality. As a result, the PSM crowd in program quality and engage the commercial media in a race to the top.

Our main model focuses on PSM and commercial media whose programs are freely available to the consumers. However, our results generalize to a model featuring both freely available and pay media, when program quality involves revealing information that the media already possess. We also discuss conditions under which our findings generalize to multidimensional strategy spaces, spillover effects of program quality on advertising revenue of other media outlets, endogenous entry and exit, and biases of PSM.4

Our paper relates to four strands of literature. First, we contribute to the literature on commercial media bias. Several empirical papers document the effect of advertising on media coverage in terms of mutual fund recommendations (Reuter & Zitzewitz, 2006), product mentions (Gambro & Puglisi, 2015), coverage of government scandals (Tella & Franceschelli, 2011) and climate change (Beattie, 2020). We present a fairly standard model of commercial media bias. Our model is in many ways similar to the models studied by (Ellman & Germano, 2009), (Germano & Meier, 2013), and (Kerkhof & Münster, 2015), as it captures bias through a program that caters to the preferences of advertisers rather than consumers. Our paper is especially close to (Ellman & Germano, 2009) and (Germano & Meier, 2013) who show that competition in media markets mitigates commercial bias, and to (Kerkhof & Münster, 2015) who find that competition between media outlets increases the likelihood that a cap on advertising quantities is welfare enhancing. Relatedly, (Blasco et al., 2016) find that if the media can raise their audience share through reducing their bias, then competition in the market may also increase the expected program quality.5 These predictions are in line with the empirical results of (Beattie et al., 2021) who find that newspapers provide less coverage of car recalls by their advertisers, but competition for readers mitigates this bias. Similarly, (Focke et al., 2016) show that commercial media bias is likely mitigated by reputational concerns on behalf of the media, e.g., if they face a demanding audience.

In contrast to the existing literature, the present study considers competition between commercial media and PSM, where PSM are not profit-maximizing, potentially regulated, and do not depend on advertising revenue to fund their operations. This allows us to inform policy debates regarding the proper role and scope of PSM in media markets. Moreover, in contrast to previous work, the present paper explicitly models competition between media outlets as a supermodular game, enabling us to draw fairly general conclusions regarding the impact of raising PSMs’ budget on the program quality provided by commercial media.

Second, we advance the broad research on the private supply of public goods (Batina & Ihori, 2005; Bergstrom et al., 1986). The provision of public goods via advertising is studied by (Anderson & Coate, 2005; Luski & Wettstein, 1994). These papers do not study media bias, however.

Third, our paper relates to the literature on supermodular games, i.e., games in which the best response of any player is increasing in the actions of its competitors (Frankel et al., 2003; Milgrom & Roberts, 1990; Topkis, 1979; Van Zandt & Vives, 2007; Vives, 1985, 1990, 2005a, 2005b). To the best of our knowledge, we are the first to apply the theory of supermodular games to a model of commercial media bias. This approach allows us to obtain fairly general results in a model with many asymmetric media outlets. Specifically, we show that in our model of commercial media bias, program qualities are strategic complements rather than strategic substitutes.

Fourth, as a consequence of strategic complementarities, public investments into program quality induce commercial media to provide high quality, too. Hence, our results support media policies that advocate financially strong PSM. In this way, we also contribute to the economics literature on PSM (see (Armstrong & Weeds, 2007b; Strömberg, 2015; Weeds, 2020) for surveys). To the best of our knowledge, the issue how PSM affect the program of commercial media has not been studied yet in the literature on commercial media bias. Other aspects of this debate have, of course, been analyzed; in addition to the empirical literature referenced above, several theoretical studies on the market impact of PSM exist. (Armstrong & Weeds, 2007a) study investments in a vertical quality dimension. (Richardson, 2006) investigates how a publicly-provided radio station offering local programs affects the provision of local programs by commercial stations. (Garcia Pires, 2016) compares program diversity in commercial versus mixed public and private duopolies. Our paper complements this line of research by studying commercial media bias. E.g., neither (Armstrong & Weeds, 2007a) nor (Richardson, 2006) consider advertisers who value program qualities in terms of (un-)biased reporting. In (Armstrong & Weeds, 2007a), viewers are ad averse and higher advertising quantities reduce viewers’ utility. PSM maximize viewer welfare, whereby viewers are better off than in a purely commercial market. However, in contrast to our paper, this is because PSM partially crowd out commercial media, whereby subscription prices and advertising quantities decrease. Similarly, (Richardson, 2006) shows that in a Hotelling model with ad averse viewers, PSM reduce profits of commercial media, but increase viewer welfare. Thus, in both models, viewers are better off because audience-friendly PSM displace commercial media. Our paper considers a different mechanism: financially strong PSM enhance viewers’ utility because they crowd in program qualities by commercial media.

The remainder of this paper is structured as follows. Section 2 introduces our theoretical framework. In Section 3, we demonstrate that program qualities in terms of unbiased reporting are strategic complements, which is our main finding, and describe the implications for crowding in effects of PSM. Section 4 considers the case where some commercial media are pay media. Section 5 discusses several extensions of our model. Section 6 concludes.

2. Model

This section introduces a fairly standard model of commercial media bias (Ellman & Germano, 2009; Germano & Meier, 2013; Kerkhof & Münster, 2015), see (Blasco et al., 2012) for a survey). Consider a model with n commercial media denoted by $1,\dots ,n$ and m PSM denoted $n+1,\dots ,n+m$. The set of commercial media is denoted by $C=\left\{1,\dots ,n\right\},$ the set of PSM is $P=\left\{n+1,\dots ,n+m\right\}.$ Each media outlet $i\in C\cup P$ chooses a program quality $v_i\in V_i\subset {\mathbb{R}}_{+}$. (An extension to multidimensional strategy spaces is considered in Section 5). Program quality $v_i$ is about unbiased reporting, i.e., about fully and truthfully reporting facts, as opposed to withholding information.6 The audience prefers high program quality, while advertisers prefer the opposite. We assume that the strategy sets $V_i$ are compact and contain $v_i=0$.

A consumer’s utility from consuming outlet i is $u_i=f_i\left(v_i\right),$ where $f_i$ is continuous, strictly increasing, and satisfies $f_i\left(0\right)=0$. Unless otherwise noted, we simply assume $f_i\left(v_i\right)=v_i.$ In Section 2 and Section 3, nothing is lost in setting $u_i=v_i;$ the distinction between utility $u_i$ and program quality $v_i$ becomes important when considering pay media or multidimensional strategies. For a commercial outlet $i\in C,$ let $u_{-i}^C=\left(u_{1,}\dots ,u_{i-1},u_{i+1},\dots ,u_n\right)$ denote the vector of the utilities of i ’s commercial competitors, $u^P=\left(u_{n+1},\dots ,u_{n+m}\right)$ the vector of utilities of the PSM, and $u_{-i}=\left(u_{-i}^C,u^P\right).$7

The size of the audience of a media outlet is denoted by $s_i.$ We impose the following assumptions.8

Assumption 1.

For all $i\in C$, $s_i$ is positive, continuous, weakly increasing in $u_i$, and weakly decreasing in $u_j$ for all $j\in P\cup C\setminus \left\{i\right\}.$

Assumption 1 is reasonable if consumers care about quality, and the media outlets are substitutes for the consumers.

Assumption 2.

For all $i\in C$, $s_i$ has weakly increasing differences in $\left(u_i,u_{-i}\right).$

If $s_i$ is twice continuously differentiable, and the strategy spaces are intervals, Assumption 2 means that

$${\displaystyle \frac{{\partial }^2}{\partial u_j\partial u_i}}{s}_i\ge 0$$

for all $j\ne i$.9 Note that Assumption 2 only assumes that the differences are weakly increasing. In particular, it is fulfilled in the case of constant differences, where the above inequality holds with equality.

As we discuss in detail in Appendix A, Assumptions 1 and 2 are satisfied by many—but not all—models for audience demand that are frequently used in media economics. For example, any model where $s_i$ is linear in $u_i$ and $u_j$ for all $j\ne i$, and does not include any interaction terms, satisfies Assumption 2 because $s_i$ has constant differences in $(u_i,u_{-i})$. This class of models comprises the Hotelling duopoly model of horizontally differentiated goods enriched by a vertical quality differentiation, and generalizations of the Hotelling model to more than two outlets such as the Spokes model and the Salop circle model. Similarly, $s_i$ has constant differences in $(u_i,u_{-i})$ in representative consumer models with quadratic utility functions. See Appendix A for the functional forms of $s_i$ in these models, and for references to publications in media economics using these specifications.

Note, however, that our assumptions are far more general than simply assuming linear demand functions. For example, when the audience demand functions include linear and quadratic terms,

$$s_i\left(u_i,u_{-i}\right)=a_i+b_i{u}_i-\sum _{j\ne i}{b}_{ij}{u}_j+\sum _k{c}_{ik}{u}_k{u}_i,$$

Assumption 2 holds as long as $c_{ik}\ge 0$ for all $i\in C$ and all $k\ne i.$

On the other hand, the logit model violates Assumption 2 whenever there are $n\ge 2$ commercial outlets. We deal with possible violations of Assumption 2 in two distinct ways. First, in Appendix F we give a sufficient condition for our main results to hold when Assumption 2 is violated, and thereby show the robustness of our results to sufficiently small violations of Assumption 2. Second, we explore our model with a weaker version of Assumption 2:

Assumption (2 log) For all $i\in C$, $ln\left(s_i\right)$ has weakly increasing differences in $\left(u_i,u_{-i}\right).$

Given Assumption 1, Assumption 2 implies Assumption (2 log), but not vice versa. For example, the logit model violates Assumption 2, but satisfies assumption (2 log) (see Appendix F). Moreover, the nested logit model—which is often used in empirical studies of audience demand in media economics (see Berry & Waldfogel, 2015 for a survey)—satisfies Assumption (2 log) as well (see Appendix F). 10 For some of our results, Assumption (2 log) is sufficient. Unless otherwise noted, below we will assume that Assumption 2 holds; we will explicitly state when we weaken it to Assumption (2 log).

Denote the advertising revenue of outlet $i,$ per member of the audience, by $R_i.$ A crucial assumption in models of advertiser bias is that, for a given audience, ad revenue depends negatively on program quality:

Assumption 3.

For all $i\in C$, $R_i$ is positive, continuous, weakly decreasing in $v_i,$ and independent of $v_j$ for all $j\ne i.$

By Assumption 3, $R_i$ is independent from the program quality of other outlets as in (Ellman & Germano, 2009) and (Kerkhof & Münster, 2015). (Germano & Meier, 2013) model spillover effects of program quality on the advertising revenue of other outlets; we will discuss spillover effects in Section 5.11

Each media outlet i has a cost $c_i\left(v_i\right)$ that may depend on its program quality.12

Assumption 4.

For all media outlets $i\in C\cup P$, $c_i$ is continuous, weakly increasing in $v_i,$ and zero at $v_i=0.$

We distinguish between two cases. First, program quality could be about fully and truthfully reporting facts that the media already have. In this case, the only cost of quality is lower advertising revenue, but there is no additional direct cost of obtaining the information in the first case. Formally, in the current model it means that $c_i\left(v_i\right)=0$ for all $v_i\in V_i$. We refer to this case as “withholding facts”. Second, program quality could also be about investigative journalism, about establishing new facts and information. Then it seems plausible that $c_i\left(v_i\right)$ is strictly increasing in $v_i.$ For example, the media might have to hire more journalists to increase program quality (see (Hamilton, 2016) for a detailed description of the economics of investigative journalism). We refer to this case as “investigating facts”.

Arguably, the case of withholding facts is highly relevant for the study of commercial media bias; indeed several papers in the literature focus on this case (Blasco et al., 2016; Ellman & Germano, 2009; Germano & Meier, 2013; Kerkhof & Münster, 2015). For instance, advertising has been known to influence editors on crucial topics such as the health risks of smoking (e.g., (Bagdikian, 2008) Chapter 12) and climate change (Beattie, 2020; Boykoff & Boykoff, 2004). The scientific facts about these topics were long well established and easily accessible, but media coverage and public perception significantly lagged in time behind the scientific consensus. Moreover, as shown in (Beattie, 2024), commercial media bias in the tone of coverage about climate change, measured based on comparisons of environmental and skeptical texts, can have important behavioral consequences, and merely changing the tone of coverage does not impact its cost.

On the other hand, pressure from advertisers may also deter media from investigating facts. Our main results on freely available media do not depend on whether we study withholding or investigating facts. For pay media, we show that the distinction matters.

Commercial media in our main model are funded by advertising, and their program is freely available for consumers; pay media will be considered in Section 4. The profit of a commercial media outlet $i=1,\dots ,n$ is (substituting $v_i=u_i$ and $v_{-i}=u_{-i}$ into $s_i)$

$${\pi }_i\left(v_i,v_{-i}\right)=s_i\left(v_i,v_{-i}\right)R_i\left(v_i\right)-c_i\left(v_i\right).$$

Commercial outlet i maximizes ${\pi }_i\left(v_i,v_{-i}\right)$ by choosing $v_i\in V_i$. Note that we disregard fixed costs which could be saved by going out of business; we defer a discussion of exit and entry to Section 5.

The PSM in our model are not-for-profit and financed independent of advertising. Their program is freely available to all consumers.13 The budget of PSM $i\in P$ is $b_i.$ We assume the PSM spend their budget to maximize consumer utility by choosing $v_i\in V_i$ subject to $c_i\left(v_i\right)\le b_i.$14 The feasible sets $V_i\subset {\mathbb{R}}_{+}$ are compact, contain $v_i=0,$ and may depend on the budget $b_i.$ We assume that a larger budget enlarges the feasible set: if $b_i<b_i^{\prime },$ then $V_i\left(b_i\right)\subseteq V_i\left(b_i^{\prime }\right).$ The model allows for inefficiencies of PSM, since different media outlets can have different cost functions and different feasible sets of program quality. We discuss potential biases of PSM in Section 5.

Some (but not all) of our considerations below impose the additional assumption that a sufficiently high program quality is necessary for a PSM to attract an audience. To express this formally, for $i\in P$ let $v_{-i}^P=\left(v_{n+1},\dots ,v_{i-1},v_{i+1},\dots ,v_{n+m}\right)$ denote the vector of program qualities of the other PSM.

Assumption 5.

A PSM outlet with zero program quality $\left(v_i=0\right)$ attracts no audience: $s_i\left(0,v^C,v_{-i}^P\right)=0$ for all $i\in P$ and $\left(v^C,v_{-i}^P\right)$, and demand for the other media outlets is as if outlet i did not exist.

Assumption 5 seems reasonable when the audience has a sufficiently attractive outside option not to consume any media. Note that under Assumption 5, a PSM with an insufficient budget cannot produce a program that attracts any audience; then the game reduces to a game between the remaining media outlets only. We will explicitly indicate where we use Assumption 5.

3. Main Results

Consider the PSM first.

Lemma 1.

A PSM i chooses

$$v_i={\overline{v}}_i\left(b_i\right):=\underset{v_i\in V_i\left(b_i\right)}{max}\left\{v_i\left|c_i\left(v_i\right)\le b_i\right.\right\}.$$

Moreover, ${\overline{v}}_i\left(b_i\right)$ is weakly increasing in $b_i,$ and independent of the strategies of the other media outlets.

Proof. 

Outlet $i\in P$ solves

$$\underset{v_i\in V_i}{max}{v}_i\mathrm{s}.\mathrm{t}.c_i\left(v_i\right)\le b_i.$$

An increase of $b_i$ relaxes the PSM’s budget constraint and enlarges the feasible set $V_i$, hence ${\overline{v}}_i$ is weakly increasing in $b_i.$ Moreover ${\overline{v}}_i$ is unique and independent of the strategies chosen by the other media outlets. □

We now turn to the commercial media. Lemma 1 allows us to view the game between the commercial media as parameterized by the budgets of the PSM $b:=\left(b_{n+1},\dots ,b_{n+m}\right)$. Let ${\overline{v}}^P\left(b\right)={\left({\overline{v}}_i\left(b_i\right)\right)}_{i=n+1}^m$ denote the vector of program qualities chosen by the PSMs. For $i\in C,$ let

$${\tilde{\pi }}_i\left(v_i,v_{-i}^C,b\right):={\pi }_i\left(v_i,v_{-i}^C,{\overline{v}}^P\left(b\right)\right)$$

and let ${\Gamma }_b=\left(C,{\left({\tilde{\pi }}_i\right)}_{i=1}^n,{\Pi }_{i=1}^n{V}_i\right)$ denote the resulting game between the commercial media outlets: the set of players is $C,$ payoff functions are ${\tilde{\pi }}_i,$ and strategy spaces are $V_i.$

To state our main result, we need the concept of a parameterized supermodular game.15 Consider a family of games with set of players $N,$ strategy spaces $X_i,$ and payoff functions $u_i$ parameterized by t in some partially ordered set of parameters values $T.$ The game $\left(N,{(u_i,{\left(X_i\right)}_{i\in N})}_{i\in N},T\right)$ is a parameterized supermodular game if, for each $i\in N:$ (i) $X_i\subseteq {\mathbb{R}}^{m_i}$ is a lattice and is compact, (ii) $u_i\left(x_i,x_{-i},t\right)$ is continuous in $x_i$ for fixed $x_{-i}$ and $t,$ (iii) $u_i\left(x_i,x_{-i},t\right)$ is supermodular in $x_i$ and has weakly increasing differences in $\left(x_i;x_{-i},t\right).$

Proposition 1.

${\Gamma }_b$ is a parameterized supermodular game.

Proof. 

The strategy spaces $V_i\subset {\mathbb{R}}_{+}$ are compact by assumption, hence compact lattices, and the objective functions ${\tilde{\pi }}_i$ are continuous in $v_i$ for fixed $v_{-i}$ and b.

Next, we show that ${\pi }_i$ has weakly increasing differences in $\left(v_i,v_{-i}\right).$ For simplicity of the exposition, we will assume here that the functions $R_i$, $s_i$ and $c_i$ are differentiable; Appendix B gives the proof without assuming differentiability. From

$${\pi }_i\left(v_i,v_{-i}\right)=s_i\left(v_i,v_{-i}\right)R_i\left(v_i\right)-c_i\left(v_i\right)$$

we obtain

$${\displaystyle \frac{\partial {\pi }_i}{\partial v_i}}={\displaystyle \frac{\partial s_i\left(v_i,v_{-i}\right)}{\partial v_i}}{R}_i\left(v_i\right)+s_i\left(v_i,v_{-i}\right)R_i^{\prime }\left(v_i\right)-c_i^{\prime }\left(v_i\right)$$

and

$${\displaystyle \frac{{\partial }^2{\pi }_i}{\partial v_j\partial v_i}}={\displaystyle \frac{{\partial }^2{s}_i\left(v_i,v_{-i}\right)}{\partial v_j\partial v_i}}{R}_i\left(v_i\right)+{\displaystyle \frac{\partial s_i\left(v_i,v_{-i}\right)}{\partial v_j}}{R}_i^{\prime }\left(v_i\right)\ge 0,j\ne i$$

(1)

where the inequality follows because of ${\displaystyle \frac{{\partial }^2{s}_i\left(v_i,v_{-i}\right)}{\partial v_j\partial v_i}}\ge 0$ by Assumption 2, ${\displaystyle \frac{\partial s_i\left(v_i,v_{-i}\right)}{\partial v_j}}\le 0$ by Assumption 1, and $R_i^{\prime }\left(v_i\right)\le 0$ by Assumption 3.

We have shown that ${\pi }_i$ has weakly increasing differences in $\left(v_i,v_{-i}\right).$ Therefore, ${\tilde{\pi }}_i$ has weakly increasing differences in $\left(v_i,v_{-i}^C\right).$ Moreover, ${\pi }_i$ has weakly increasing differences in $\left(v_i,v^P\right).$ It remains to show that ${\tilde{\pi }}_i$ has weakly increasing differences in $\left(v_i,b\right).$ By Lemma 1, ${\overline{v}}_k\left(b_k\right)$ is increasing in $b_k,$ while ${\overline{v}}_{k^{\prime }}$ does not depend on $b_k$ for $k^{\prime }\ne k.$ Since ${\pi }_i$ has weakly increasing differences in $\left(v_i,v^P\right),$ it follows that ${\tilde{\pi }}_i$ has weakly increasing differences in $\left(v_i,b\right).$ □

Proposition 1 shows that the program qualities are strategic complements. The economics of the result is straightforward. The fundamental trade-off for a commercial outlet in a model of commercial media bias is as follows: providing a program in line with the preferences of the audience attracts a bigger audience, but leads to lower advertising revenue per consumer. If the program qualities of competing media increase, the audience of a given outlet is smaller, hence also the implicit cost of increasing its own program quality. The logic is closely related to the finding in (Germano & Meier, 2013) that withholding facts typically increases with the concentration of ownership on the media market, which has found empirical support in (Beattie et al., 2021).

Note that violations of Assumption 2 do not necessarily overturn Proposition 1. In Appendix F, we give a sufficient condition for Proposition 1 to hold if Assumption 2 is violated. Moreover, a different sufficient condition is available in the case of hiding information:

Corollary 1.

Suppose that Assumptions 1, (2 log), and 3 hold. Consider the case of hiding information, i.e., $c_i\left(v_i\right)=0$ for all $v_i\in V_i$. Suppose that $s_i$ and $R_i$ are strictly positive for all $\left(v_i,v_{-i}\right)\in V_i\times V_{-i}$. Then ${\Gamma }_b$ is a parameterized supermodular game.

Proof. 

We only give the proof assuming differentiability for simplicity. Commercial outlet i maximizes ${\pi }_i(v_i,v_{-}i)=s_i(v_i,v_{-}i)R_i\left(v_i\right)$. By assumption, $s_i(v_i,v_{-}i)R_i\left(v_i\right)>0.$ Thus the profit maximizing quality of firm i also has to maximize

$$ln{\pi }_i=ln{s}_i+ln{R}_i.$$

Since $ln{s}_i$ has weakly increasing differences by Assumption (2 log), and $R_i$ is independent of $v_j$ for $j\ne i$, it follows that $ln{\pi }_i$ has weakly increasing differences in $\left(v_i,v_{-i}\right).$ The rest of the proof is as in the proof of Proposition 1. □

The logit model, and the nested logit model, are two frequently used audience demand functions in media economics. As mentioned above, they satisfy Assumption (2 log). Corollary 1 thus implies that in the case of hiding information our main results apply to the (nested) logit model.

Leveraging the theory of supermodular games (see (Vives, 2005a), (Vives, 2005b) or (Sarver, 2023) for expositions) allows us to generate fairly general results in our model featuring many asymmetric media outlets. Denote a strategy profile in game ${\Gamma }_b$ by $v^C=\left(v_1,\dots ,v_n\right).$ The following corollary collects standard results for parametrized supermodular games that are useful in our context:

Corollary 2.

If ${\Gamma }_b$ is a parameterized supermodular game, then ${\Gamma }_b$ has, for any $b,$ a lowest equilibrium $v^{C,low}$ and a highest equilibrium $v^{C,high},$ such that any equilibrium $v^C$ satisfies $v^{C,low}\le v^C\le v^{C,high}.$ Moreover, the equilibria $v^{C,low}$ and $v^{C,high}$ are weakly monotone increasing in $b.$

In particular, an equilibrium exists; the standard proof for equilibrium existence in supermodular games uses the Tarski fixed point theorem. Turning to the comparative statics, note Corollary 2 does not imply that all equilibria are monotone increasing in b: only the highest and lowest equilibria are guaranteed to be weakly monotone increasing in b (see (Sarver, 2023) for a general elaboration of this point for supermodular games).16 When the equilibrium is unique, a stronger monotone comparative static result is available, which we highlight in the following Proposition 2.

Proposition 2.

Suppose ${\Gamma }_b$ is a parameterized supermodular game and has a unique equilibrium. Then the equilibrium program quality of each commercial media outlet $i\in C$ is weakly increasing in the budget $b_j$ of any PSM $j\in P$.

Proposition 2 states that PSM do not crowd out, and may even crowd in program quality, in line with the idea that PSM engage commercial media in a race to the top. To illustrate the result, we compare a “dual” (or mixed public and commercial) media market, featuring both PSM and n commercial media outlets, with a purely commercial media market consisting only of the same n commercial outlets, postponing considerations about entry to Section 5. Under Assumption 5, Proposition 2 implies that in a “dual” media market, the program of the commercial media outlets is weakly more audience-friendly and weakly less advertiser-friendly than when there are only the n commercial media. To see this, recall that when $b_i$ is insufficient, the PSM i cannot attract any audience in our model by Assumption 5, and then the resulting competition between the remaining media is as if PSM i was not on the market. Applying Proposition 2 shows that the program qualities of the commercial media will be weakly lower in this situation than when there are viable PSM.

A sufficient condition for uniqueness of the equilibrium can be given from the contraction approach: If the profit functions ${\tilde{\pi }}_i$ are smooth and strictly quasiconcave in $v_i,$ a sufficient condition for equilibrium uniqueness is that

$${\displaystyle \frac{{\partial }^2{\tilde{\pi }}_i}{\partial v_i^2}}+\sum _{\begin{array}{c}j\ne i\\ j\in C\end{array}}\left|{\displaystyle \frac{{\partial }^2{\tilde{\pi }}_i}{\partial v_i\partial v_j}}\right|<0$$

for all $\left(v_i,v_{-i}\right)$(Vives, 1999, Chapter 2.5). In Appendix I, we use the contraction approach to spell out sufficient conditions for equilibrium uniqueness with a linear audience function $s_i,$ and in the case of withholding information with a logit audience function.

The monotone comparative statics results provided so far do not rule out the possibility that the quality of a commercial outlet remains constant when the budget of a PSM increases, for example because the set of possible qualities $V_i$ could be discrete, or because of corner solutions or kinks in the profit function. Moreover, so far nothing in our assumptions guarantees that a larger budget of a PSM translates into strictly higher quality.17 Following (Edlin & Shannon, 1998), we now provide a strict monotone comparative statics result by adding assumptions on interior solutions and differentiability and employing “strict” versions of Assumptions 1 and 3 above. Note we do not assume that $s_i$ has strictly increasing differences, however.

Corollary 3.

Suppose that $V_i=\left[0,v_i^{high}\right]$ with $v_i^{high}>0$ for all media outlets i. Moreover, suppose that for all $j\in P$, a higher budget $b_j$ strictly increases $v_j^{high}$. For each commercial outlet $i\in C$, assume that ${\pi }_i(v_i,v_{-i})$ is differentiable, $s_i(v_i,v_{-i})$ is strictly decreasing in $v_j$ for each $j\ne i$ whenever $s_i(v_i,v_{-i})>0$, and $R_i\left(v_i\right)$ is strictly decreasing in $v_i$. Suppose ${\Gamma }_b$ is a parameterized supermodular game and has a unique equilibrium, which is interior in the sense that $0<v_i<v_i^{high}$ and $0<s_i<1$ for all $i\in C.$ Then the equilibrium program quality of each commercial media outlet $i\in C$ is strictly increasing in the budget $b_j$ of any PSM $j\in P$.

Proof. 

Outlet $j\in P$ solves

$$\underset{v_j\in V_j}{max}{v}_j\mathrm{s}.\mathrm{t}.c_j\left(v_j\right)\le b_j.$$

An increase of $b_j$ relaxes the PSM’s budget constraint and strictly enlarges the feasible set $V_j=\left[0,v_j^{high}\right]$ by strictly increasing $v_j^{high}$. Hence ${\overline{v}}_j$ is strictly increasing in $b_j.$

Moreover, under the current assumptions, inequality (1) in the proof of Proposition 1 holds with strict inequality because ${\displaystyle \frac{\partial s_i\left(v_i,v_{-i}\right)}{\partial v_j}}<0$ and $R_i^{\prime }\left(v_i\right)<0$ by the current assumptions. That is, ${\pi }_i$ has strictly increasing marginal returns in $(v_i,v_j)$, holding constant all other $v_k,k\ne i,k$, and hence (by the strict monotone comparative statics results of Edlin & Shannon, 1998) the best reply of each commercial outlet i strictly increases in $b_j$. The new equilibrium must therefore involve strictly higher qualities of all commercial outlets. □

4. Pay Media

This section studies an extension to the model where some commercial media outlets are pay media, i.e., they earn revenue from direct payments from consumers. Suppose that media outlets $i\in C^f=\left\{1,\dots ,n_f\right\}$ are freely available: they are funded solely by advertising and “free” in the sense that consumers do not pay a monetary price for consumption. Outlets $i\in C^{pay}\in \left\{n_f+1,\dots ,n\right\}$ are pay media. The set of all commercial media is $C=C^f\cup C^{pay}$.18 As above, outlets $i\in P=\left\{n+1,\dots m\right\}$ are PSM.

A pay media outlet $i\in C^{pay}$ chooses program quality $v_i\in V_i$ and price $p_i\in P_i$. In this section, we focus on the case where $V_i=\left[0,v_i^{high}\right]$ and $P_i=\left[0,p_i^{high}\right]$, with $v_i^{high}>0$ and $p_i^{high}>0,$ and assume that functions are smooth and solutions are interior19, and that there is a unique $v_i^{*}\in V_i$ such that $R_i^{\prime }\left(v_i^{*}\right)=-1$. To obtain a strict monotone comparative static result, we also assume that for all $i\in C$, $s_i$ is strictly decreasing in $u_j$ for $j\ne i$ as long as $s_i>0$.

Utility from consuming outlet i is $u_i=v_i-p_i,$ utility from consuming an outlet $j\in C^f\cup P$ is simply $u_j=v_j.$

The profit of a pay media outlet $i\in C^{pay}$ is

$${\pi }_i\left(v_i,p_i,u_{-i}\right)=s_i\left(u_i,u_{-i}\right)\left(R_i\left(v_i\right)+p_i\right)-c_i\left(v_i\right),$$

where $u_{-i}$ is the vector of utilities offered by the other outlets. The profit of a freely available media outlet $i\in C^f$ is

$${\pi }_i\left(u_i,u_{-i}\right)=s_i\left(u_i,u_{-i}\right)R_i\left(v_i\right)-c_i\left(v_i\right).$$

In all other respects, the model is as in Section 2 above.

For pay media, results depend on whether we consider the case of withholding or investigating facts (see the discussion after Assumption 4 above). Results are clear cut in the case of withholding facts, where $c_i\left(v_i\right)=0$ for all $v_i.$ We show that in this case, when some competitor $j\ne i$ increases the utility $u_j$, outlet i will also offer a higher utility: pay media keep their program quality constant but lower their price, while freely available media increase their program quality. We briefly discuss the case of investigating facts towards the end of this section.

Lemma 2.

Consider the case of withholding information where $c_i\left(v_i\right) =0$ for all $v_i\in V_i$ and all $i\in C^{pay}.$ Then outlet $i\in C^{pay}$ will choose program quality $v_i=v_i^{*}$, independent of the strategies of the other media outlets. Moreover, the price $p_i$ is strictly decreasing in $u_j$ for $j\ne i$, holding constant the strategies of the remaining outlets $k\ne i,j$.

Proof. 

The first order conditions for an interior solution are

$$\begin{array}{ccc}\hfill {\displaystyle \frac{\partial {\pi }_i}{\partial v_i}}& =& {\displaystyle \frac{\partial s_i\left(v_i-p_i,u_{-i}\right)}{\partial u_i}}\left(R_i\left(v_i\right)+p_i\right)+s_i\left(v_i-p_i,u_{-i}\right)R_i^{\prime }\left(v_i\right)=0,\hfill \\ \hfill {\displaystyle \frac{\partial {\pi }_i}{\partial p_i}}& =& -{\displaystyle \frac{\partial s_i\left(v_i-p_i,u_{-i}\right)}{\partial u_i}}\left(R_i\left(v_i\right)+p_i\right)+s_i\left(v_i-p_i,u_{-i}\right)=0.\hfill \end{array}$$

Rearranging the second line and inserting it into the first gives, after dividing by $s_i>0,$

$$1+R_i^{\prime }\left(v_i\right)=0.$$

Therefore, firm i chooses $v_i=v_i^{*}$ defined by $R_i^{\prime }\left(v_i^{*}\right)=-1.$

Plugging $v_i=v_i^{*}$ into the first order condition for $p_i$ gives

$$-{\displaystyle \frac{\partial s_i\left(v_i^{*}-p_i,u_{-i}\right)}{\partial u_i}}\left(R_i\left(v_i^{*}\right)+p_i\right)+s_i\left(v_i^{*}-p_i,u_{-i}\right)=0.$$

By the implicit function rule, the sign of the reaction of $p_i$ on $u_j$ ($j\ne i)$ is equal to

$$-{\displaystyle \frac{{\partial }^2{s}_i\left(v_i^{*}-p_i,u_{-i}\right)}{\partial u_j\partial u_i}}\left(R_i\left(v_i^{*}\right)+p_i\right)+{\displaystyle \frac{\partial s_i\left(v_i^{*}-p_i,u_{-i}\right)}{\partial u_j}}>0,$$

where the inequality follows because of ${\displaystyle \frac{{\partial }^2{s}_i\left(u_i,u_{-i}\right)}{\partial u_j\partial u_i}}\ge 0$ by Assumption (2), $R_i\left(v_i^{*}\right)\ge 0$ and $p_i>0,$ and ${\displaystyle \frac{\partial s_i\left(u_i,u_{-i}\right)}{\partial u_j}}<0$ by assumption.

□

Lemma 2 allows us to consider the game as one where the pay media have only one choice variable: the price. To find the profit maximizing prices, substitute $v_i=v_i^{*}$ into the profit function of outlet $i\in C^{pay}.$ Instead of maximizing profits by choosing $p_i,$ we can equivalently think of firm i as choosing utility $u_i,$ taking into account that $u_i=v_i^{*}-p_i$.

The set of utilities that outlet i can choose from is $U_i:=\left\{u_i\left|u_i=v_i^{*}-p_i,p_i\in P_i\right.\right\}$. The objective function is

$${\widehat{\pi }}_i\left(u_i,u_{-i}\right):=s_i\left(u_i,u_{-i}\right)\left(R_i\left(v_i^{*}\right)+v_i^{*}-u_i\right).$$

Mirroring our definitions leading to Proposition 1 above, let

$${\tilde{\pi }}_i\left(u_i,u_{-i}^C,b\right)=\left\{\begin{array}{cc}{\pi }_i\left(u_i,u_{-i}^C,{\overline{v}}^P\left(b\right)\right),& \mathrm{if}i\in C^f,\\ {\widehat{\pi }}_i\left(u_i,u_{-i}^C,{\overline{v}}^P\left(b\right)\right),& \mathrm{if}i\in C^{pay}.\end{array}\right.$$

Let ${\Gamma }_b^{pay}=\left(C,{\left({\tilde{\pi }}_i\right)}_{i=1}^n,{\Pi }_{i=1}^{n_f}{V}_i\times {\Pi }_{i=n_f+1}^n{U}_i\right)$ denote the resulting game between the commercial media outlets: the set of players is $C=C^f\cup C^{pay},$ payoff functions are ${\tilde{\pi }}_i,$ outlets $i\in C^f$ chooses $u_i\in V_i,$ outlets $i\in C^{pay}$ choose $u_i\in U_i$ while their program quality is fixed at $v_i^{*}$ by Lemma 2, and as above the utilities offered by the PSM are given by ${\overline{v}}^P\left(b\right).$

Proposition 3.

In the case of withholding information where $c_i\left(v_i\right) =0$ for all $v_i\in V_i$ and all $i\in C^{pay}$, ${\Gamma }_b^{pay}$ is a parameterized supermodular game.

Proof. 

To begin with, since $P_i$ is compact, the set of feasible utilities $U_i$ is compact as well. The rest of the proof follows similar lines as the proofs of Proposition 1 and Lemma 2. For $i\in C^{pay}$ and $j\ne i,$

$$\begin{array}{cc}\hfill {\displaystyle \frac{{\partial }^2{\widehat{\pi }}_i}{\partial u_j\partial u_i}}& ={\displaystyle \frac{\partial }{\partial u_j}}\left({\displaystyle \frac{\partial s_i\left(u_i,u_{-i}\right)}{\partial u_i}}\left(R_i\left(v_i^{*}\right)+v_i^{*}-u_i\right)-s_i\left(u_i,u_{-i}\right)\right)\hfill \\ \hfill & ={\displaystyle \frac{{\partial }^2{s}_i\left(u_i,u_{-i}\right)}{\partial u_j\partial u_i}}\left(R_i\left(v_i^{*}\right)+v_i^{*}-u_i\right)-{\displaystyle \frac{\partial s_i\left(u_i,u_{-i}\right)}{\partial u_j}}>0\hfill \end{array}$$

where the inequality follows because of ${\displaystyle \frac{{\partial }^2{s}_i\left(u_i,u_{-i}\right)}{\partial u_j\partial u_i}}\ge 0$ by Assumption (2), $R_i\left(v_i^{*}\right)\ge 0$, $v_i^{*}-u_i=p_i\ge 0,$ and ${\displaystyle \frac{\partial s_i\left(u_i,u_{-i}\right)}{\partial u_j}}<0$ by assumption. The remainder of the proof is similar to the proof of Proposition 1. □

Proposition 3 shows that ${\Gamma }_b^{pay}$ has weakly increasing reaction functions. That is, when some competitor of a commercial media outlet i increases the utility it offers, ceteris paribus outlet i will also offer a higher utility. For a pay media outlet $i\in C^{pay}$, program quality is constant by Lemma 2, but i strictly lowers its price. The economics behind the result is straightforward: tougher competitors reduce residual demand, and as a reaction firm i charges a lower price. Proposition 3 also shows that the freely available media will, as in Section 3 above, ceteris paribus react to increases in the utility offered by a competitor by weakly increasing their program quality.

As above, we can leverage the theory of supermodular games to obtain results on ${\Gamma }_b^{pay}$. In particular, Proposition 2 generalizes in the following way:20

Proposition 4.

Consider the case of withholding information where $c_i\left(v_i\right) =0$ for all $v_i\in V_i$ and all $i\in C^{pay}$, and suppose that ${\Gamma }_b^{pay}$ has a unique equilibrium. Then an increase of the utility $u_j$ of consuming a PSM $j\in P$ will weakly increase the utilities $u_i$ offered by all commercial outlets: the program qualities of freely available media weakly increase, the program qualities of pay media stay constant but their prices decline.

A sufficient condition for uniqueness of the equilibrium can be given by applying the contraction approach to the game ${\Gamma }_b^{pay}$.

To conclude this section, we briefly consider to the case of investigating facts. We point out that the assumption that $c_i\left(v_i\right) =0$ is crucial for our above results. If $c_i$ is strictly increasing in $v_i,$ then the equilibrium program quality of firm i can be strictly decreasing in $u_{-i},$ and the total effect of $u_{-i}$ on $u_i$ is ambiguous, as we show in example in Appendix C below. We leave a full exploration of pay media in the case of investigating facts for future research.

5. Discussion

Of course, our model abstracts away from several issues that could potentially be relevant. In this section, we discuss multidimensional strategy spaces, spillover effects of program quality on the advertising revenue of other media outlets, entry, and potential biases in PSM. We focus on freely available media, and assume differentiability wherever convenient for expositional simplicity. Formal analyses are deferred to the Appendix.

5.1. Multidimensional Strategy Spaces

Media outlets may report differently on different topics, and may choose other dimensions of program quality that are less of a concern for advertisers. E.g., media outlet i could report on current events such as climate change, economic developments like changes in bank rates, and sports events like the football world cup. Advertisers from carbon-emitting industries might be concerned about high program quality on the topic of climate change, and indifferent about program qualities of the remaining topics. Advertisers from the sportswear industry might be concerned about full reporting on the production conditions of football gear, and indifferent about full reporting on tax evasion by football players. Media outlet i could choose high program quality on all, several, or none of these topics. How does this affect our results?

Suppose that outlet i reports about $k_i$ topics, and let $v_{i,k}$ denote program quality of topic $k.$21 We assume that $v_{i,k}\in \left[0,v_{i,k}^{high}\right]$ with $v_{i,k}^{high}>0.$ Outlet i thus chooses a vector $v_i\in V_i={\times }_{k=1}^{k_i}\left[0,v_{i,k}^{high}\right].$ Consumer utility from consuming outlet i is $u_i=f_i\left(v_i\right),$ where $f_i$ is continuous, strictly increasing with respect to each argument $v_{i,k}$, and satisfies $f_i\left(0\right)=0$. Advertising revenue per consumer is $R_i\left(v_i\right),$ where $R_i:V_i\to {\mathbb{R}}_{+}$ is positive, continuous, weakly decreasing in each argument $v_{i,k},$ and independent of $v_{-i}.$ The profit of $i\in C$ is ${\pi }_i=s_i\left(u_i,u_{-i}\right)R_i\left(v_i\right)-c_i\left(v_i\right).$ Turning to the PSM, suppose that $i\in P$ chooses $v_i\in V_i\left(b_i\right)$ to maximize $u_i=f_i\left(v_i\right)$ subject to $c_i\left(v_i\right)\le b_i.$ As above, a higher budget may enlarge the feasible set $V_i$.

5.1.1. Withholding Facts

In the following, it is important to distinguish between withholding facts and investigating facts. In the case of withholding facts, there are no direct costs of raising program quality. Thus, $c_i\left(v_i\right)=0$ for all $v_i\in V_i$ and all $i\in C$, and our results generalize. See Appendix D.1 for a formal analysis.

5.1.2. Investigating Facts

In the case of investigating facts, $c_i\left(v_i\right)$ is strictly increasing in $v_i$ for all $i\in C$. Trivially, as long as the game remains supermodular, our results generalize. A relevant concern is, however, whether profit ${\pi }_i$ will be supermodular in its own choice variables.

We illustrate this with a two-dimensional case inspired by (Germano & Meier, 2013). Suppose that outlet i chooses program quality $v_i\in V_i=[0,v_i^{high}]$ and general quality $y_i\in Y_i=[0,y_i^{high}]$. The general quality $y_i$ captures all dimensions of quality except (un-)biased reporting (e.g., quality of exposition or pleasing visuals) and does not affect $R_i$.

Appendix D.2 demonstrates that ${\pi }_i$ has weakly increasing differences in $\left(\left(v_i,y_i\right),\left(v_{-i},y_{-i}\right)\right)$. For a supermodular game, however, ${\pi }_i$ must be supermodular in $\left(v_i,y_i\right)$, too. Whether or not this is the case depends on the cost function $c_i$ and the utility function $f_i.$

If there are sufficiently strong economies of scope in producing $\left(v_i,y_i\right),$ or if there are sufficiently strong complementarities between $v_i$ and $y_i$ for the consumers, then ${\pi }_i$ is supermodular in $\left(v_i,y_i\right).$ If this is the case for all commercial outlets $i\in C,$ our main results generalize. In contrast, if there are no complementarities between $v_i$ and $y_i$ stemming from $c_i$ or $f_i$, and $s_i$ is concave in $u_i$, profit ${\pi }_i$ will be submodular in $\left(v_i,y_i\right)$. In this case, the effect of a higher budget for the PSM on the utility of the audience from consuming commercial media is ambiguous, as we show by example in Appendix D.3.

5.2. Spillover Effects of Program Qualities on Advertising Revenue of Other Media Outlets

Our main model assumes that the advertising revenue of a commercial media outlet depends on its own program quality, but not on the program qualities of other media outlets. Arguably, advertising revenue of all outlets might be negatively affected when some outlets report about deficiencies of a product, hence there may be spillover effects as in (Germano & Meier, 2013). We show in Appendix E.1 that our results are robust when these spillover effects are small compared to the direct effect of an outlet’s own program quality on its advertising revenue. If spillover effects were as strong as the direct effects, however, the strategic complementarities between the outlets’ program qualities could diminish, resulting in program qualities becoming independent of each other (see Appendix E.2).

5.3. Entry and Exit

Our results on strategic complementarities apply to situations where the PSM do not induce any of the commercial outlets to exit the market. In reality, when the PSM budgets are sufficiently increased, commercial outlets may be driven out of business. By the same token, if PSM were scaled back, this could trigger entry of additional commercial outlets. The new entrants would have to provide sufficiently high quality in order to overturn the results in Proposition 2, however.

To illustrate, suppose the PSM were abolished in favor of a purely commercial media market. Without additional entry, our results above predict that program quality of the commercial outlets would decline. Entry of m additional commercial outlets would keep the number of media outlets constant. If these entrants offer lower program quality than the PSM used to, however, incumbent commercial media will still provide lower program quality than before the commercialization of the media market. Consequently, all consumers are negatively affected by lower program qualities. Whether there will be enough entrants with sufficiently high program quality to overcome this negative effect on consumers will depend on various factors, including barriers to entry, the revenue potential of the market, the PSMs’ budgets and hence quality, and potentially cost advantages or disadvantages of new entrants.

In Appendix G, we study a Hotelling example with one PSM and one potential commercial entrant, and compare the equilibrium qualities with those in a purely commercial duopoly. The example illustrates the importance of the quality of the PSM in comparison to the equilibrium qualities in a purely commercial market: If the PSM quality is lower, then because of the strategic complementarities the commercial outlet will also have a lower quality than in a purely commercial market. Similarly, if the PSM quality is higher but not too high, the quality of the private outlet will also be higher than in a purely private market. On the other hand, if the quality of the PSM is too high, it crowds out the commercial media outlet.

5.4. Biases in PSM

Our model allows PSM to be cost-inefficient but assumes them to be commercially unbiased, i.e., they choose a program that is as audience-friendly as possible, given their budget. Of course, PSM may also be biased (e.g., Crawford & Levonyan, 2018). In particular, PSM also engage in advertising and product placement, and therefore their content may be influenced by advertisers. Moreover, in some countries, governments are major advertisers themselves, making PSM susceptible to government influence (Tella & Franceschelli, 2011). E.g., (Szeidl & Szucs , 2021) and (Bátorfy & Urbán, 2020) document large advertising favors from the Hungarian government to national media outlets, and large corruption coverage favors from the privileged media to the government in return. Similarly, (Yanatma, 2021) reports that the Turkish government has recently emerged as the media’s largest advertiser and has used its power to shape the media’s reporting.22

While such considerations are clearly important, we point out that our results can allow for some biases in PSM. The strategic complementarities between the program qualities of PSM and commercial media do not depend on assumptions about the PSM at all. The key issue is whether a higher budget of a PSM will translate into more or less severe biases of this outlet. As long as the program qualities of PSM are increasing in their budgets—i.e., as long as the programs become more audience-friendly when funding of PSMs increases—, Propositions 1 and 2 are robust, no matter if the advertiser is a political player or not. If more government spending induces PSM to withhold more critical information about political deficits, however, the PSMs’ program quality would decrease, and thereby also the program quality of their commercial competitors.23

As in our discussion of entry above, any evaluation of the impact of potentially biased PSM on the program of commercial media outlets crucially depends on what the alternatives to PSM are. PSM are typically not for profit, and they often face tighter limitations on advertising than commercial outlets (see e.g., (Crawford et al., 2017)), which may counteract commercial media bias (Kerkhof & Münster, 2015). Indeed, PSM typically have a higher share of hard news and socially relevant topics in their program, so their commercial biases may be lower (see (Cushion, 2017) for a wide ranging review). On the other hand, advertising revenue helps against other sources of biases in media content (see for example (Besley & Prat, 2006; Petrova, 2011), and (Szeidl & Szucs, 2021)).

6. Conclusions

In this paper, we show that in a model of commercial media bias, program qualities in terms of unbiased reporting are strategic complements rather than strategic substitutes. The strategic complementarity stems from the media’s fundamental trade-off in these models: Increasing program quality increases the value of the program for the audience but decreases the willingness to pay of the advertisers to reach consumers. The latter effect becomes less important when a media company has a smaller audience; hence, its incentives to increase program qualities are higher. Thus, in a media market with both PSM and commercial media, PSMs’ with high program qualities give commercial media incentives to provide high quality themselves, too. As a result, the PSM crowd in quality and engage the commercial media in a race to the top. This is in line with recent empirical evidence on public and private investments into program quality (Sehl et al., 2020; Simon, 2013).

Our results hold under fairly general conditions. One important assumption is that audience demand functions have weakly increasing differences, a condition met by various standard demand functions. These include linear demand functions, quadratic demand functions with positive coefficients for the interaction terms, as well as models such as Hotelling, Salop, and Spokes. We also give sufficient conditions for our results to hold for audience demand functions that do not have weakly increasing differences, such as the logit model. While our main analysis considers media outlets who offer their programs for free, our results also extend to pay media when commercial media bias is about withholding facts that the media already have. Similarly, our results hold for multidimensional strategy spaces in the case of withholding facts; for the case of investigating facts, we provide conditions under which our main results generalize. Arguably, advertising revenue of all outlets might be negatively affected when some outlets report about deficiencies of a product, hence there may be spillover effects. However, we show that our results are robust when these spillover effects are small compared to the direct effect of an outlet’s own program quality on its advertising revenue. If entry or exit of commercial media was possible, commercial entrants would have to provide sufficiently high quality in order to overturn our main results. Finally, we point out that our results can allow for some biases in PSM as long as a higher budget of a PSM will translate into less severe biases of this outlet.

We have also show, however, that program qualities are not always strategic complements. We give examples that show that, for pay media (or multidimensional strategy spaces) in the case of costly investigative journalism, higher quality PSMs can increase or decrease the quality of commercial media outlets, depending on details of the model. Moreover, strong PSM may prevent entry of commercial outlets in the first place. Furthermore, higher budgets for PSMs could, in case of politically captured PSMs, increase their biases, and by strategic complementarities the biases of commercial media would increase as a consequence.

The paper contributes to recurrent media policy debates about the proper role and scope of PSM. While several regulation authorities fear that raising the program quality of PSM could crowd out private investments into program quality, our results support policies that advocate strong and financially well-equipped PSM. Reductions in the funding of PSM might result in a worse media landscape altogether.

Our insights might be especially important for modern media markets like social media, where systematic quality controls are missing and quality standards are often claimed to be low (Zhuravskaya et al., 2020). While PSM have typically played a minor role here, our results encourage PSM to develop a stronger presence and provide high-quality content on social media, too. This reasoning is in line with recent scholarly advances calling on PSM to become “Public Service Internet platforms” with the objective to provide opportunities for public debate, participation, and the advancement of social cohesion (Unterberger & Fuchs, 2021).

An interesting avenue for future research would be to test our predictions empirically. In particular, we hypothesize that an increase in PSMs’ budget would ceteris paribus translate both into higher program qualities of the PSM themselves as well as into higher program qualities of the PSMs’ commercial competitors. Similarly, reductions in PSM budgets would lead to lower program qualities of both PSM and commercial media. However, the identification of a causal relationship between PSM budgets and program qualities would require some exogenous variation in PSM budgets.