How Media Competition Fuels the Spread of Misinformation

Arash Amini; Eun-Ju Lee; Radu Marculescu; Ufuk Topcu; Yigit Ege Bayiz; Zeynep Somer-Topcu

REVIEW 4 major objections 5 minor 77 references

How Media Competition Fuels the Spread of Misinformation

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that competition between ideologically opposed groups of news sources rationally produces misinformation-heavy strategies for hyper-partisan outlets, public polarization, and a misinformation arms race.

desk verdict A novel and honest model of media competition and misinformation, but its central empirical claim rests on an assumed radicalization objective and a qualitative fit — worth serious peer review, with major revision required. read the letter →

arxiv 2411.15677 v1 pith:OBIAFDPD submitted 2024-11-24 cs.SI

Arash Amini , Yigit Ege Bayiz , Eun-Ju Lee , Zeynep Somer-Topcu , Radu Marculescu , Ufuk Topcu This is my paper · ORCID

classification cs.SI

keywords misinformationmediacompetitionopiniondynamicsquantalresponseequilibriumzero-sumgamesourcecredibilitypolarizationexposure

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

News outlets that compete for public influence face a dilemma: sharing misinformation boosts immediate attention but erodes their credibility. This paper models that trade-off as a zero-sum sequential game between two coalitions of ideologically opposed sources, solved with the quantal response equilibrium, a standard account of boundedly rational decision-making. It claims that in equilibrium, hyper-partisan outlets rationally disseminate more misinformation than centrist ones, reproducing the credibility-bias pattern seen in real-world media ratings. It further claims that competition creates a misinformation arms race—when one side increases misinformation, the opposing side's best response is to do the same—and that these dynamics polarize public opinion. The payoff is a strategic explanation for why misinformation persists despite its reputational costs, together with levers for intervention.

What carries the argument

The central object is a zero-sum sequential game coupling two dynamic processes. Source credibility evolves as a convex combination of past credibility and the current factual-or-misinformation action, $c_{t+1} = \lambda c_t + (1-\lambda) a_t$, and individual opinions evolve under social influence (an exponential-decay homophily kernel) plus media influence, whose multiplier $\psi(r,c,a,s) = \exp[-\hat{\kappa}(1+\eta a)(1+\zeta(1-c)(1-s)) r]$ encodes the attention gain from misinformation ($\eta$) and the credibility penalty ($\zeta$). The solution concept is the quantal response equilibrium of this entropy-regularized game, which captures bounded rationality; the equilibria are computed with the extragradient method on an empirically estimated payoff matrix. The running reward $r(x_t,c_t) = -\sum_i \sin(\frac{\pi}{2} x_i^t)^5$ is what makes the game zero-sum and encodes the assumption that players seek to radicalize public opinion toward their own pole while treating swing voters as undesirable.

What would settle it

Replace the reward in Eq. (6) with an audience-reach proxy, such as the total number of influenced individuals regardless of opinion, keep every other equation and parameter fixed, and recompute the quantal response equilibrium; if hyper-partisan sources no longer disseminate the most misinformation, the paper's explanation of real-world misinformation rests entirely on the radicalization objective rather than on competition itself.

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Extended reading notes

Core claim

The paper's central discovery is that competition for public influence between two ideologically opposed coalitions of news sources has quantal-response equilibria in which the optimal strategy for hyper-partisan sources is to disseminate misinformation often, while centrist sources preserve credibility by sharing mostly factual content. This equilibrium pattern matches the credibility-by-bias distribution observed in real-world news-source ratings without any curve fitting: it emerges from the structural incentives of the game. The same equilibria show that misinformation polarizes the opinion distribution into echo chambers, and that deviations by one player—such as increasing misinformation output—are met by the opposing player's optimal response of also increasing misinformation, producing a reciprocal arms race. The model also predicts a phase transition: if the short-term attention gain from misinformation is reduced enough, or the long-term credibility penalty increased, the equilibrium flips, depolarizing the community but sharply raising average misinformation exposure because centrist sources then become the main misinformation spreaders.

Load-bearing premise

The load-bearing premise is the reward function, which assumes media players maximize the ideological radicalization of the public (via $r(x_t,c_t)=-\sum_i \sin(\frac{\pi}{2} x_i^t)^5$) rather than audience reach, advertising revenue, or per-source credibility.

Editorial extensions

If this is right

Reducing the short-term engagement payoff of misinformation—for example by debunking from within the same partisan community—is predicted to be more effective at depolarizing public opinion and lowering exposure than merely increasing penalties on source credibility.
A single low-credibility source can disrupt the equilibrium and trigger a system-wide escalation: the opposing coalition's optimal response is to increase its own misinformation output, producing a lose-lose outcome for both sides.
Improving community media literacy (lowering susceptibility) tends to depolarize, but pushing susceptibility too low can flip the equilibrium into a phase where centrist sources become the main misinformation spreaders and average exposure spikes.
As players become more rational (approaching Nash equilibrium), the equilibrium becomes more polarized, implying that misinformation-heavy hyper-partisan strategies are calculated responses to the competitive landscape rather than mistakes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the radicalization reward were replaced by a profit- or reach-maximizing objective, the qualitative results might change substantially; comparing those equilibria would reveal how much of the misinformation outcome is driven by the assumed payoff versus the structure of competition.
The arms-race prediction implies a testable natural experiment: if one outlet's misinformation output exogenously increases (for example, after a credibility-rating event), competitors' misinformation rates should subsequently rise; if they do not, the equilibrium response mechanism is incomplete.
The model assumes susceptibility is fixed, but psychological evidence of an illusory-truth effect suggests exposure to misinformation can itself raise susceptibility; incorporating that feedback would likely strengthen the self-reinforcing spread and could shift the phase-transition threshold.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this paper deserves a serious referee, but the referee should push for major revision. The genuinely new piece is the integration: a credibility-susceptibility opinion dynamics model (Eqs 1–3) coupled to a zero-sum quantal response equilibrium over media strategies, plus the arms-race comparative static and the intervention analysis. That combination is not in the cited literature, and the paper is transparent about what it does and does not do. The sensitivity analysis around misinformation gain, credibility gain, rationality, and susceptibility is exactly the kind of exploration that makes a modeling paper useful.

The soft spots are real, and I largely agree with the stress-test. Eq (6) is load-bearing and asserted, not derived. The reward −Σ sin((π/2)x_i)^5 means both players want to radicalize the public and actively dislike swing voters. Under that objective, misinformation is attractive despite the credibility penalty. That gives a coherent conditional result — if media outlets maximize ideological radicalization, then competition pushes them toward misinformation — but the paper keeps stating the unconditional version. The zero-sum assumption in Eq (5) further builds in the adversarial frame. Without robustness checks against alternative objectives like audience reach, advertising revenue, or credibility maximization, the headline claim about competition is not established.

Second, the empirical validation is qualitative. The match to the Ad Fontes credibility-bias curve is visual. The complete-action equilibrium does not reproduce the smooth curve; the paper says so and introduces a hand-picked limited action set (Fig 4e) that does. That is an honest limitation, but it weakens the claim that the model “reproduces” real-world distributions. There is no code, no data, no convergence diagnostics for the QRE solver, and several parameters appear only inside the text. The stability statement is also based on a local function approximation.

Credit where due: the paper cites the right adjacent literatures — strategic disinformation games, opinion dynamics, media competition — and the self-citations are not padding. The writing is clear, and the authors flag the main modeling simplifications themselves.

For whom: computational social scientists and misinformation policy people will get value from the model and the sensitivity results, but they should treat the equilibrium predictions as hypotheses. Recommendation: accept for peer review, require major revision. The referee should ask for a derivation or empirical grounding of Eq (6), robustness to alternative objectives, quantitative fit statistics, and code/data release.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes a computational game-theoretic model of news-source competition. Two coalitions ('left' and 'right') choose, at each time step, whether each source under their control disseminates factual news or misinformation. Source credibility evolves according to Eq. (1), individual opinions by the stochastic social-media interaction in Eq. (2), and media influence by Eq. (3). The competition is formulated as a zero-sum sequential game (Eq. 5) with the running reward in Eq. (6), which rewards moving public opinion to the ideological extremes. The authors solve for quantal response equilibria numerically, first with a complete action space and then with a restricted set of strategy profiles (Fig. 4e), and report that equilibrium play reproduces the Ad Fontes-style credibility-bias relation, that misinformation polarizes opinion and creates echo chambers, that one player's increased misinformation leads the opponent to increase misinformation as well, and that sensitivity analysis identifies possible interventions.

Significance. Conditional on the modeling assumptions, the paper offers an integrative framework and produces falsifiable comparative statics, such as phase transitions in the misinformation gain η and credibility gain ξ, and monotone effects of rationality τ. The use of quantal response equilibrium to model bounded rationality is appropriate for the problem, and the authors are transparent about the local-solution limitation of their function approximation. If the central mechanism were robust, the paper would be a useful proof of concept that competitive equilibria can rationalize hyper-partisan misinformation. However, the headline empirical claim is only qualitative, the core mechanism is substantially encoded in the payoff, and the numerical results are not accompanied by code, data, or convergence diagnostics. The significance as a statement about real media competition is therefore not yet established.

major comments (4)

[Equilibrium Concept, Eq. (6)] The reward function r(xt,ct) = -Σ_i sin((π/2)x_i^t)^5 assumes that media players seek to radicalize public opinion: it is maximized at the extremes and minimized at the center, and the text explicitly says swing voters are undesirable and ϑ=5 is chosen to make centrist opinions low-reward. This radicalization-seeking objective is asserted rather than derived from observed media-firm goals such as audience size, advertising revenue, or credibility maximization. Since Eq. (5) is zero-sum and Eq. (6) is the only payoff, the results that equilibrium play involves misinformation, polarization, and an arms race are largely consequences of this assumed objective. The central claim that competition fuels misinformation therefore requires either an empirical defense of Eq. (6) or a robustness analysis with alternative, empirically grounded objectives.
[Results, Fig. 4] The claimed reproduction of the real-world credibility-bias distribution is qualitative and partly built into the action set. The complete-action equilibrium in Fig. 4(a) produces sharp credibility transitions, and the authors concede that this result is 'contrary to the real-world credibility distributions'; they then introduce the limited action set in Fig. 4(e). The nine profiles in Fig. 4(e) are hand-selected strategy profiles that already have a smooth credibility-bias shape, so the equilibrium selecting among them cannot be presented as independent evidence that the model reproduces Fig. 1(a). No goodness-of-fit statistic, error bar, or comparison to a null model is provided. As it stands, the abstract's claim that 'the resulting equilibria for this game reproduce the credibility-bias distribution' is not supported by the evidence.
[Results, Fig. 5] The game in Eq. (5) is symmetric between the two players: the payoff depends only on the opinion vector and not on which player controls which sources. A symmetric zero-sum game cannot endogenously generate a systematic difference in misinformation policies between the two parties without an explicit symmetry-breaking mechanism such as asymmetric initial conditions, asymmetric susceptibility, or asymmetric action sets. The paper nevertheless suggests that its findings explain the partisan imbalance in misinformation exposure documented by Mosleh and Rand. This inference is unsupported without such a mechanism or a clear statement of what breaks the symmetry in the simulations.
[Quantal Response Equilibrium and Results] The central equilibrium results are numerical but not reproducible from the manuscript. The value function is approximated with function approximation, the payoff matrix is estimated empirically through 200 simulations, and the extragradient method is used; however, the paper provides no code, data, hyperparameter ranges, random seeds, or convergence diagnostics. Figure 7 further states that increasing τ makes the quantal response equilibrium computation unstable, and the text notes that function approximation methods typically find local solutions. The assertion that the reported equilibrium is stable is therefore not verifiable from the material supplied. Given that the paper's main conclusions rest on these computations, this is a load-bearing gap.

minor comments (5)

[Eq. (3)] The parameter for credibility gain is written as ζ in Eq. (3) but as ξ in the surrounding text and in later sensitivity analysis; this inconsistency should be fixed throughout.
[Eq. (6)] The reward is written as r(xt,ct), but the right-hand side depends only on xt, not on ct; either remove the unused argument or define the dependence.
[Eq. (8)] The notation R(qt) is introduced without definition; it should be connected to the running reward defined in Eq. (6) or defined explicitly.
[Information Structure and Equilibrium Concept] The text says that player R controls sources with ym < 0, which duplicates the definition of player L; the second occurrence should presumably read ym > 0.
[Throughout] There are several typos and stylistic errors, including 'influnced', 'also remains also', and inconsistent subfigure references in the Figure 2 caption; a careful proofread is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline results are computed consequences of an explicit radicalization objective, not restatements of the inputs.

full rationale

The paper's derivation chain is self-contained. The reward function in Eq (6) is an explicit modeling premise: players are assumed to maximize radicalized public opinion. This premise is strong and may be empirically contestable, but it is not a hidden restatement of the conclusions. The equilibrium, best-response, and sensitivity results are computed from the stated model via Eqs (8)-(10) and numerical simulation, not fitted to the real-world data. The comparison to Fig 1(a) is an external validation; the unrestricted equilibrium already yields the central-sources-higher-credibility trend, and the limited action set in Fig 4(e) is introduced as a tractability and realism simplification, not shown to encode the target credibility-bias distribution. Self-citations (refs 10, 13, 14, 15, 20) are background or prior technical tools and are not load-bearing for the central claim. The concern that the radicalization objective drives the misinformation and polarization conclusions is a premise-strength or external-validity issue, not a circularity: the model does not define 'competition' as 'misinformation spread' nor equate any fitted parameter with a headline prediction. Therefore no circular step is exhibited.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The model introduces no new physical entities. Its explanatory burden is carried by hand-set parameters (eta, xi, beta, kappa, h) and domain assumptions, especially the radicalization-seeking reward function and the content-blind influence assumption. The credibility construct is a modeled variable rather than an invented entity.

free parameters (7)

eta (misinformation gain) = 1
Set by hand in 'Opinion Dynamics in Presence of Misinformation'; controls the attention boost from misinformation and is a key determinant of the phase transitions in Fig 6.
xi (credibility gain) = 2
Set by hand; controls the credibility penalty in psi and interacts with eta to determine whether misinformation or credibility dominates.
beta1, beta2 (susceptibility distribution shape) = 3, 2
Chosen ad hoc for the beta distribution of individual susceptibility; shifts the balance between susceptible and resilient users.
kappa, kappa_hat (homophily coefficients) = 20, 5
Chosen ad hoc; control exponential decay of social and media influence over opinion distance.
h, sigma (influence amplitude and noise) = h=0.1, sigma=0.1*sqrt(h)
Chosen ad hoc; scale the opinion update and stochastic disturbance in Eq (2).
lambda (community memory parameter) = not specified
Appears in the credibility update Eq (1) but no numerical value is given; simulation results depend on it.
gamma (discount factor) = not specified
Appears in the game objective Eq (5) but no numerical value is given; the equilibrium depends on it.

assumptions (5)

ad hoc to paper Media players maximize radicalization of public opinion and devalue swing voters, via r(x) in Eq (6).
This objective is assumed without empirical support and directly leads to polarization-seeking strategies.
domain assumption Individuals are influenced by news based only on source credibility and their own susceptibility, not on the content of the news.
Explicitly acknowledged in 'Individual Susceptibility'; encoded in psi in Eq (3).
domain assumption Credibility evolves as a convex combination of past credibility and current factualness, starting at perfect credibility 1 (Eq 1).
Initial perfect credibility and the memory parameter lambda create the early advantage for misinformation.
domain assumption Competition is zero-sum between two coordinated team players, each controlling half of the sources.
Reduces heterogeneous media competition to two opposing teams; no utility for total audience size except through ideological influence.
standard math Quantal response equilibrium with entropy regularization is the solution concept (Eqs 8-10).
Standard QRE formalism; existence and uniqueness follow from known results, though computation is approximate.

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Pith. "Pith review of How Media Competition Fuels the Spread of Misinformation." pith.science (2026). https://pith.science/paper/OBIAFDPD

@misc{pith2026241115677,
  author       = {Pith},
  title        = {Pith review of: How Media Competition Fuels the Spread of Misinformation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OBIAFDPD}},
  note         = {Machine review of arXiv:2411.15677}
}

read the original abstract

Competition among news sources may encourage some sources to share fake news and misinformation to influence the public. While sharing misinformation may lead to a short-term gain in audience engagement, it may damage the reputation of these sources, resulting in a loss of audience. To understand the rationale behind sharing misinformation, we model the competition as a zero-sum sequential game, where each news source influences individuals based on its credibility-how trustworthy the public perceives it-and the individual's opinion and susceptibility. In this game, news sources can decide whether to share factual information to enhance their credibility or disseminate misinformation for greater immediate attention at the cost of losing credibility. We employ the quantal response equilibrium concept, which accounts for the bounded rationality of human decision-making, allowing for imperfect or probabilistic choices. Our analysis shows that the resulting equilibria for this game reproduce the credibility-bias distribution observed in real-world news sources, with hyper-partisan sources more likely to spread misinformation than centrist ones. It further illustrates that disseminating misinformation can polarize the public. Notably, our model reveals that when one player increases misinformation dissemination, the other player is likely to follow, exacerbating the spread of misinformation. We conclude by discussing potential strategies to mitigate the spread of fake news and promote a more factual and reliable information landscape.

Figures

Figures reproduced from arXiv: 2411.15677 by the authors.

**Figure 1.** a. The credibility with respect to political bias for 223 news sources from Ad-Font websites. The hyper-partisan sources are less credible compared to the centrist ones. b. Normalized media influence intensity with respect to news source credibility and individual susceptibility. Credibility becomes irrelevant for susceptible individuals. c-f. Visualization of how credibility and disseminating misinformation affect … view at source ↗

**Figure 2.** Opinion dynamics become polarized when news source strategies for disseminating misinformation reflect real-world policies. a,e. Evolution of opinions among N = 500 individuals for two different strategies c,g. with η = 1, ξ = 2, β1 = 3, β2 = 2. b,f. Snapshots of susceptibility and opinion distribution over time steps t = {0,100,200}. Initially, hyper-partisan sources start with high credibility while frequently dis… view at source ↗

**Figure 3.** Different candidates for the reward function r(x). The players seek to radicalize public opinion in their favor and minimize the influence of the opponent. The exponent of the reward function controls players’ preference for radicalization. Larger exponents (red, green) indicate a stronger preference for radicalized public opinion. Public opinion becomes polarized when news sources employ the strategy reported by Ad… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: The equilibrium for M2 actions a,b. and nine selected actions c,d.. Both cases entirely polarize public opinion, but the complete action achieves greater separation between peaks. (b) The evolution of opinion when each source can choose any action at each time for the …

**Figure 5.** Figure 5: Whenever a player increases misinformation dissemination below equilibrium, the other player’s optimal response causes it to share more misinformation. a. The left player changes its policy to share more misinformation by deviating from equilibrium, while the right pla…

**Figure 6.** Figure 6: Reducing attention gained from misinformation may cause a phase transition c. in equilibrium that depolarizes public opinion and exacerbates misinformation exposure. a. Bimodality coefficient for different values of misinformation gain, η and credibility gain ξ . The g…

**Figure 7.** Figure 7: Increasing rationality leads to more polarized equilibrium. a. Bimodality coefficient for different levels of rationality, τ. b. Slices showing opinion distributions of users at equilibrium for τ = {1, 10, 100} and Nash Equilibrium (τ → ∞). Increasing τ makes the quant…

**Figure 8.** Figure 8: Decreasing community susceptibility can depolarize a susceptible community. However, it could result in more misinformation exposure for individuals. a,b. bimodality coefficient and misinformation exposure for different susceptibility distributions. c-g. Final opinion …

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