A Simple Model of Online Platform Enshittification

This is a model of “Green-Daying”:= services often start out as a core product with a well-defined set of features for a target user-base, and slowly morph into a generic, engagement-hungry machine. A notable example of ‘green daying’ is the Eternal September of 1993: Usenet begane experiencing a perpetual influx of new users from AOL overwhelmed the established community norms, and the “September” that once ended each year as college students settled in, suddenly never did. Green Day even wrote a maudlin song about it, and for good measure demonstrated this phenomenon with their career, which was charmingly meta of them.

This note presents a simple model showing how rational, profit-maximizing platforms can be incentivized to actively generate their own Eternal September. This is a first attempt at following Hal Varian’s advice on economic models as finger-exercises for the mind that convey a specific point. It primarily serves as a first attempt at formalizing the tyranny of the marginal user, the carcinization property of tech, and the influential but (afaict) entirely informal innovator’s dilemma by Clayton Christensen.

Some speculations about implications for consumer LLMs conclude the post. The depracation and eventual un-deprecation of the supine GPT-4o model last week worryingly suggests there might be something to this.

Model Setup

Users

• A continuum of potential users indexed by $i\in [0,1]$.
• Each user $i$ has a set of base preferences $({\alpha }_i^0,{\beta }_i^0)$.
  • ${\alpha }_i^0$: The user’s base utility from participation (extensive margin).
  • ${\beta }_i^0$: The user’s base marginal utility from usage (intensive margin).
• These preferences are distributed according to a joint distribution $\mathbb{F}({\alpha }^0,{\beta }^0)$.

The Platform

• The platform makes two strategic choices:

  1. A subscription price $p\ge 0$.
  2. A design parameter $\theta \in [0,1]$.

• The design parameter $\theta$ affects user utility. A higher $\theta$ represents a strategic choice to cater more to marginal, high-engagement users at the expense of inframarginal, high-participation-value users. Higher $\theta$s could correspond with more popularity bias, e.g. ‘slop’ in recommendations, for example. In other words, it represents a shift along a spectrum from a niche/curated experience to a mainstream/algorithmic one.

  • Effective participation utility: ${\alpha }_i(\theta )={\alpha }_i^0(1-\theta )$
    • As $\theta$ increases, the value derived from the platform’s unique, curated identity diminishes.
  • Effective usage utility: ${\beta }_i(\theta )={\beta }_i^0(1-\theta )+{\beta }_m\theta$
    • Here, ${\beta }_m$ is an exogenous parameter representing Mainstream Engagement Utility. It’s the high marginal utility that a generic, algorithmically-optimized, “slop” feed provides to the broad market.
    • As $\theta$ increases, a user’s utility from usage becomes less about their specific niche interests (${\beta }_i^0$) and more about the universal, high-engagement appeal of the mainstream design (${\beta }_m$).

User’s Problem

Utility Function

The utility for user $i$ from using the platform for $h_i$ hours, given a design $\theta$ and price $p$, is:

$$U_i(h_i,\theta ,p)={\alpha }_i(\theta )\cdot 1\{h_i>0\}+{\beta }_i(\theta )\cdot h_i-\frac{\delta }{2}{h}_i^2-p\cdot 1\{h_i>0\}$$

Where:

• $1\{h_i>0\}$ is an indicator function that is 1 if the user subscribes and 0 otherwise.
• $\delta$ is a parameter representing the diminishing returns to usage (cost of attention/time).

User’s Optimization Problem

The user makes two decisions: whether to subscribe, and if so, how much to use the platform.

Step 1: Optimal Usage (Intensive Margin)

If a user subscribes ($h_i>0$), they choose their usage level $h_i$ to maximize their utility. The first-order condition (FOC) is:

$$\frac{\partial U_i}{\partial h_i}={\beta }_i(\theta )-\delta h_i=0$$

This gives the optimal usage, conditional on subscribing:

$$h_i^{\ast }(\theta )=\frac{{\beta }_i(\theta )}{\delta }$$

Step 2: Subscription Decision (Extensive Margin)

A user will subscribe if the utility from participating with their optimal usage is greater than their outside option (normalized to 0). We substitute $h_i^{\ast }$ back into the utility function to find the utility from subscribing:

$$U_i(h_i^{\ast },\theta ,p)={\alpha }_i(\theta )+{\beta }_i(\theta )\left(\frac{{\beta }_i(\theta )}{\delta }\right)-\frac{\delta }{2}{\left(\frac{{\beta }_i(\theta )}{\delta }\right)}^2-p$$ $$U_i(h_i^{\ast },\theta ,p)={\alpha }_i(\theta )+\frac{{\beta }_i(\theta {)}^2}{2\delta }-p$$

The participation condition is:

$${\alpha }_i(\theta )+\frac{{\beta }_i(\theta {)}^2}{2\delta }>p$$

Market Aggregates

The continuum of users lets us write these as integrals over the distribution of user preferences.

Demand Function (Number of Subscribers)

The total number of subscribers, $N$, is the integral over all users who satisfy the participation condition:

$$N(\theta ,p)={\int }_{i=0}^{1}1\left\{{\alpha }_i(\theta )+\frac{{\beta }_i(\theta {)}^2}{2\delta }>p\right\}di$$

Total Platform Usage

The total usage across all subscribers, $H$, is the integral of optimal usage $h_i^{\ast }$ for all users who subscribe:

$$H(\theta ,p)={\int }_{\text{subscribers}}{h}_i^{\ast }(\theta )di={\int }_{i=0}^1\frac{{\beta }_i(\theta )}{\delta }\cdot 1\left\{{\alpha }_i(\theta )+\frac{{\beta }_i(\theta {)}^2}{2\delta }>p\right\}di$$

Platform’s Profit Maximization

Profit Function

The platform’s profit, $\Pi$, consists of subscription revenue and potentially advertising revenue, minus the cost of design quality. A key strategic decision for the platform is whether to “turn on” advertising.

Let the advertising revenue per hour of user engagement, $a$, be a choice variable for the platform, where $a\in \{0,a_{max}\}$.

• $a=0$: The platform is a pure subscription service.
• $a=a_{max}>0$: The platform chooses to monetize engagement through ads. We can think of this as a “break glass to get ad revenue” action.

The platform’s profit, $\Pi$, is therefore:

$$\Pi (\theta ,p,a)=p\cdot N(\theta ,p)+a\cdot H(\theta ,p)-C(\theta )$$

Where:

• $C(\theta )$ is the cost of implementing design $\theta$, with $C^{\prime }(\theta )>0$.

Optimization Problem

The platform chooses $\theta ,p$ and $a$ to maximize its profit:

$$\underset{\theta \in [0,1],p\ge 0,a\in \{0,a_{max}\}}{\max }\Pi (\theta ,p,a)$$

Characterizing the Equilibrium

Assumptions

1. $C(\theta )$ is strictly convex with $C(0)=0$, $C^{\prime }(0)=0$, and $C^{\prime \prime }(\theta )>0$
2. $F({\alpha }^0,{\beta }^0)$ has continuous density with compact support
3. Regularity: Assume ${\beta }_m$ lies in the upper-middle range of the ${\beta }^0$ distribution (e.g., 70th percentile),

• ensuring that $\partial H/\partial \theta >0$ while preserving heterogeneity in user preferences.

Existence Result

Proposition: An equilibrium $({\theta }^{\ast },p^{\ast },a^{\ast })$ exists for any $a\in \{0,a_{max}\}$.

Comparative Statics

Proposition: Let ${\theta }^{\ast }(a)$ denote the equilibrium design parameter when advertising level is a. Then:

• ${\theta }^{\ast }(0)<{\theta }^{\ast }(a_{max})$ (advertising increases design homogenization)
• The user base composition shifts from high-$\alpha$/low-$\beta$ to low-$\alpha$/high-$\beta$ as a increases

First-Order Conditions

The optimal $({\theta }^{\ast },p^{\ast })$ is found by taking the partial derivatives of the profit function and setting them to zero.

1. FOC with respect to Price ($p$):

$$\frac{\partial \Pi }{\partial p}=N(\theta ,p)+p\frac{\partial N}{\partial p}+a\frac{\partial H}{\partial p}=0$$

Interpretation: The platform increases the price until the marginal revenue from a price hike on existing users ($N(\theta ,p)$) is exactly offset by the loss in revenue from users who unsubscribe ($p\frac{\partial N}{\partial p}$) and the corresponding loss in advertising revenue from their departure ($a\frac{\partial H}{\partial p}$).

2. FOC with respect to Design ($\theta$):

$$\frac{\partial \Pi }{\partial \theta }=p\frac{\partial N}{\partial \theta }+a\frac{\partial H}{\partial \theta }-C^{\prime }(\theta )=0$$

Interpretation: The platform adjusts its design $\theta$ until the marginal revenue generated by the change equals its marginal cost. The marginal revenue comes from two sources: the change in subscription revenue as the set of subscribers changes ($p\frac{\partial N}{\partial \theta }$) and the change in advertising revenue as total user engagement changes ($a\frac{\partial H}{\partial \theta }$). This is balanced against the marginal cost of the design change, $C^{\prime }(\theta )$.

Dynamic Implications of the Model

The Advertising Catalyst

The platform’s trajectory is critically determined by its decision to monetize engagement. The choice to set $a>0$ acts as a powerful catalyst, unleashing the tyranny of the marginal user and dictating the platform’s evolution.

Let’s re-examine the FOC for design, $\theta$, now that $a$ is a choice:

$$\frac{\partial \Pi }{\partial \theta }=p\frac{\partial N}{\partial \theta }+a\frac{\partial H}{\partial \theta }-C^{\prime }(\theta )=0$$

Assumption: For the user population, base preferences are negatively correlated, i.e., $\text{Cov}({\alpha }^0,{\beta }^0)<0$. This means users are broadly either “hobbyists” (high ${\alpha }^0$, low ${\beta }^0$) or “normies” (low ${\alpha }^0$, high ${\beta }^0$), where the former group has high extensive margin utility from using the service but lower marginal utility from engagement, while the latter group is the opposite. This captures the empirical observation that users who highly value platform identity (high ${\alpha }^0$) tend to have lower engagement needs (low ${\beta }^0$), and is a substantively important assumption.

Case 1: Pure Subscription Model ($a=0$)

If the platform forgoes ad revenue, its incentive for adjusting $\theta$ is driven solely by how design changes affect the number of subscribers ($p\frac{\partial N}{\partial \theta }$). The platform might still increase $\theta$ slightly to capture some high-$\beta$ users, but the incentive is weak and balanced against the risk of losing high-$\alpha$ users. The equilibrium ${\theta }^{\ast }$ will likely be low.

Case 2: The “Break Glass” Moment (Setting $a=a_{max}>0$)

When a platform activates advertising, the equation changes dramatically. A new, powerful term emerges: $a\frac{\partial H}{\partial \theta }$. The platform is no longer just optimizing for participation, but also for total time spent.

This is the catalyst for the tyranny:

1. Strengthened Incentive: The term $\frac{\partial H}{\partial \theta }$ is strongly positive. Increasing $\theta$ boosts the usage of high-$\beta$ users, who contribute the most to total hours, $H$. The platform now has an enormous financial incentive to increase $\theta$.
2. Shift in Focus: The platform’s optimization problem shifts from “how do we get more subscribers?” to “how do we get more engagement?“.
3. The Inevitable Squeeze: As established, increasing $\theta$ attracts high-$\beta$ users while penalizing the high-$\alpha$ “hobbyists” by reducing their core participation utility. The introduction of advertising revenue makes this trade-off heavily skewed. The platform is now willing to lose several low-engagement “hobbyists” if it can gain a single high-engagement “normie” whose ad-impression revenue more than compensates for the lost subscription fees.

The decision to “break glass” and turn on advertising is not a minor tweak; it fundamentally rewrites the platform’s objective function. It transforms the platform from a service catering to participation value into an engine optimized for engagement, thereby accelerating the shift in its user base and leading it directly down the path of alienating its initial supporters. The most prominent consumer LLMs are all likely hovering their hands over the hammer to break glass.

Evolution of the User Base: Hemorrhaging hobbyists

The tyranny of the marginal user is not a static condition; it implies a dynamic process of user base evolution. A user leaves not because of a separate “exit function,” but because the platform’s evolving strategy makes their participation condition no longer hold.

Let’s trace the dynamic over time periods $t=0,1,2,...$:

1. Initial State ($t=0$): A new platform launches with a neutral design, ${\theta }_0\approx 0$, and no advertising, $a_0=0$. It attracts a base of “hobbyist” users (high ${\alpha }^0$, low ${\beta }^0$) who value its core proposition and are willing to pay price $p_0$. For these users, ${\alpha }_i({\theta }_0)+\frac{{\beta }_i({\theta }_0{)}^2}{2\delta }>p_0$.

2. Growth Phase ($t=1$): To grow, the platform activates its ad-based model ($a_1=a_{max}$) and looks to the marginal user. This user is likely a “normie” (low ${\alpha }^0$, high ${\beta }^0$). To attract them, the platform increases its design parameter to ${\theta }_1>{\theta }_0$. This strategic shift successfully brings in a new cohort of high-engagement users.

3. The Squeeze ($t=2$ and beyond): As the platform continues to optimize for growth and engagement revenue, it keeps pushing ${\theta }_t$ higher. Consider the participation condition for an original “hobbyist” user under the new regime ${\theta }_t$:

   • Their participation utility, ${\alpha }_i({\theta }_t)={\alpha }_i^0(1-{\theta }_t)$, strictly decreases as ${\theta }_t$ rises.
   • Their usage utility, ${\beta }_i({\theta }_t)$, changes little because their base ${\beta }_i^0$ is low. The benefit from the quadratic term is minimal.

   Eventually, the platform’s strategy will reach a point where, for this “hobbyist,” the condition reverses:

   $${\alpha }_i({\theta }_t)+\frac{{\beta }_i({\theta }_t{)}^2}{2\delta }<p_t$$

   At this moment, the user churns. The platform is actively hemorrhaging its initial, high-value “hobbyist” users. Its user base is not just growing; its composition is fundamentally shifting from high-$\alpha$, low-$\beta$ types towards low-$\alpha$, high-$\beta$ types.

An Opening for Disruption: The Innovator’s Dilemma

This dynamic of hyper-fixating on the marginal, high-engagement user creates the classic conditions for Christensen’s Innovator’s Dilemma, which is a famous (entirely verbal) model of the risks of following marginal customers into corners. The incumbent platform becomes so optimized for serving its most profitable (high-$\beta$) user segment that it creates an opening for a competitor to serve the neglected segment.

1. The Underserved Market:

The hobbyists who have been pushed out, along with those who were never attracted to the incumbent’s high-$\theta$ strategy, form a coherent, underserved market. They value curation and participation utility ($\alpha$) and are repelled by the features that cater to mindless engagement ($\beta$).

2. The Challenger’s Strategy:

A new challenger platform can enter the market not by competing with the incumbent on its own terms, but by doing the opposite. The challenger’s optimal strategy would be to target the underserved hobbyists with:

• A design choice of ${\theta }_c\approx 0$ (the $c$ subscript denotes the challenger). This maximizes the ${\alpha }_i={\alpha }_i^0(1-{\theta }_c)$ term that these users value.
• A simple subscription price $p_c$, and crucially, a commitment to no advertising ($a_c=0$).

However, if it manages to enter the market, it will face its own break-glass-to-get-ad-revenue problem and will become a slop merchant too.

3. The Disruption Condition:

We don’t formally model the challenger’s problem but simply assert that there is a pool of observant challengers that will enter when a condition is fulfilled. The market is ripe for disruption if a challenger can enter and be profitable. A user $i$ will switch from the incumbent or join the challenger if the utility from the challenger is greater than both the incumbent and the outside option. The potential profit for the challenger is ${\Pi }_c=p_c\cdot N_c({\theta }_c,p_c)-C({\theta }_c)$.

We can define a Disruption Condition: The incumbent’s strategy $({\theta }^{\ast },p^{\ast },a^{\ast })$ is vulnerable to disruption if there exists a challenger strategy $({\theta }_c,p_c,a_c=0)$ such that:

$${\Pi }_c({\theta }_c,p_c,a_c=0)>0$$

Why the Incumbent is Trapped:

The incumbent’s management is not foolish; they see this opening. However, responding would require them to lower their own ${\theta }^{\ast }$ and, more importantly, turn off their advertising revenue ($a^{\ast }=0$). This would mean sacrificing the enormous profits they make from their large, high-engagement user base to compete for the smaller, less (engagement-)profitable hobbyist market. The incumbent’s own profit-maximization framework paralyzes it, leaving the door open for the challenger to establish a foothold.

Limitations

The primary results in this note arise out of qualitatively motivated assumptions of (1) users having quadratic utility, and (2) distributional assumptions on $\mathbb{F}(\cdot )$, namely the negative correlation between ${\alpha }_i$ and ${\beta }_i$. (1) can be relaxed to any utility function that is concave with a finite maximum, and possesses super-linear relationship between the maximized intensive margin utility and the user’s inherent usage propensity ${\beta }_i$. (2) can be reasoned about and parametrized with a covariance matrix $\Sigma$.

Extensions

The Role of Pricing Structure: Mitigating or Accelerating the Curse

The analysis thus far has assumed a simple subscription model (a fixed fee $p$), which is a form of a one-part tariff. However, platforms can choose other pricing structures, such as a two-part tariff or a pure usage-based model. This choice is not neutral; it fundamentally alters the platform’s incentives and can either dampen or amplify the “curse of the marginal user.”

Let’s reconsider the platform’s problem under two alternative pricing schemes.

Two-Part Tariff: Profit $=F+t\cdot h_i$

In a two-part tariff, the platform chooses a fixed access fee $F$ (like a subscription) and a per-unit usage fee $t$.

• User’s Problem: The user’s cost is now $F+t\cdot h_i$. The optimal usage $h_i^{\ast }$ is found where the marginal benefit equals the marginal cost: ${\beta }_i(\theta )=t+\delta h_i$, which gives $h_i^{\ast }=({\beta }_i(\theta )-t)/\delta$.
• Participation Condition: A user joins if ${\alpha }_i(\theta )+({\beta }_i(\theta )-t{)}^2/(2\delta )>F$.
• Platform’s Profit: $\Pi (\theta ,F,t,a)=F\cdot N+(t+a)\cdot H-C(\theta )$.

Implication: Mitigating the Curse.

The two-part tariff is a powerful price discrimination tool. It allows the platform to capture surplus from both user types simultaneously:

• It can capture surplus from high-$\alpha$ “hobbyists” through the fixed fee $F$.
• It can capture surplus from high-$\beta$ “normies” through the usage fee $t$.

Because the platform can directly monetize high engagement via $t$, it has less incentive to distort the entire platform design via $\theta$ to cater exclusively to high-engagement users. It can maintain a more moderate $\theta$ to keep the “hobbyists” on the platform (and paying $F$) while still profiting from the “normies” (who pay $t$ on their high usage). The two pricing levers ($F$ and $t$) give the platform the flexibility to serve a heterogeneous user base without having to go “all-in” on one user type. This structure, therefore, mitigates the curse of the marginal user.

Pure Usage-Based Pricing: Profit = $t\cdot h_i$

This is a special case of the two-part tariff where the fixed fee $F=0$. This model is common for infrastructure platforms (e.g., cloud computing).

• User’s Problem: The barrier to entry is zero. A user participates as long as they derive some positive utility from usage.
• Platform’s Profit: $\Pi (\theta ,t,a)=(t+a)\cdot H-C(\theta )$.

Implication: Maximally Accelerating the Curse.

In this model, the platform’s revenue is entirely and exclusively a function of total usage $H$. The participation utility ${\alpha }_i$ becomes almost irrelevant to the platform’s bottom line. The platform’s singular goal is to maximize engagement.

This creates the strongest possible incentive to increase $\theta$ to cater to the highest-$\beta$ users, as they are the only ones who generate significant revenue. Any user with a low ${\beta }_i$ (the “hobbyist”) is essentially a freeloader from the platform’s perspective. The design will aggressively evolve to serve the high-engagement segment, pushing all other user types away. This pricing structure represents the purest acceleration of the curse.

Conclusion: The Coming September for Large Language Models

This model provides a lens through which to view the evolution of today’s most promising technology: consumer-facing Large Language Models. How might the Eternal September play out here?

The “Slop Dial” $\theta$ for an LLM could be its degree of obsequiousness and verbosity.

• Low $\theta$: The LLM is a tool. Its responses are concise, dense, and technically accurate. It is optimized for power users and developers who value efficiency and predictability. a low $\theta$ LLM is a razor-sharp coding and mathematical assistant.
• High $\theta$: The LLM is an assistant, a therapist, and a confidante. Its responses are verbose, obsequious, chatty, caveated, and replete with summaries, disclaimers, and conversational filler (“Certainly, here is the information you requested…”, “You’re absolutely right …”, “This is not X — it is Y”). This makes the LLM much worse for its original users.

The “hobbyists” are developers who want a clean API. The “normies” are the mass market of users who may perceive verbosity and hand-holding as higher quality or more helpful.

As LLM companies face immense pressure to justify their valuations and find mass-market product-market fit, the incentive to turn up the $\theta$ dial is enormous. Catering to the marginal, less-sophisticated user by making the model more verbose and obsequious can increase perceived value across the broadest possible audience. This risks alienating the power users who were its initial champions and who are most sensitive to the loss of information density.

Observing the evolution of models like ChatGPT, Claude, and Gemini through this lens will be fascinating. The gradual shift in their default behavior may not be an accident, but a rational, profit-driven slide into an Eternal September of their own making.