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Raising Rivals' Costs on Hybrid Platforms: The Complementarity of Fees and Self-Preferencing

This paper demonstrates that on hybrid platforms, fees and self-preferencing act as strategic complements, meaning that regulating either instrument effectively curbs the other to prevent higher prices and reduced consumer welfare, even when such practices pass conventional antitrust tests.

Original authors: Maysam Rabbani, Ram Sewak Dubey

Published 2026-08-05

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Maysam Rabbani, Ram Sewak Dubey

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, bustling digital town square where anyone can set up a stall to sell their wares. This is the world of "hybrid platforms," the online marketplaces that have become the backbone of modern shopping. In this town, the owner of the square does two things at once: they manage the stalls for independent sellers (the "third-party" vendors), and they also run their own shop right in the middle of the square (the "first-party" shop). The owner collects a tax from the independent sellers for every item they sell, but their own shop pays no tax. To make things interesting, the owner also controls the town's loudspeakers and spotlight, deciding which products get the best view and which get hidden in the back.

For years, regulators and economists have worried that if they try to stop the owner from using the loudspeakers to favor their own shop, the owner might just crank up the taxes on everyone else to compensate. It's like a parent worrying that if they stop a sibling from gaining an unfair advantage at a game, the sibling will just start a new, meaner rule. This paper dives deep into that specific worry. It asks a simple but tricky question: Do these two tools—the tax and the spotlight—work against each other, or do they work together? The answer changes everything about how we should police these digital giants.

The Digital Town Square: A Tale of Two Tools

Let's step into the shoes of the owner of this massive online marketplace. Think of the platform as a giant, invisible mall. Inside, there are thousands of independent sellers (let's call them "Shopkeepers") and the mall owner's own private brand (let's call it "Mall Brand"). The Mall Brand is special because it doesn't have to pay the entry fee that the Shopkeepers do.

The Mall Brand owner has two main levers to pull to make sure their own products win:

The Fee (The Tax): They charge the Shopkeepers a percentage of every sale. This makes the Shopkeepers' goods more expensive, pushing customers toward the tax-free Mall Brand.
Self-Preferencing (The Spotlight): They tweak the search algorithms and recommendation lists so that the Mall Brand appears at the very top, while the Shopkeepers get pushed down to the second or third page.

For a long time, people thought these two levers were like a seesaw. The idea was: "If you take away the spotlight, the owner will just crank up the tax to make up for it." It seemed like a game of "Whack-a-Mole"—fix one problem, and the other pops up worse.

But this paper flips that script entirely. The authors built a mathematical model of this town square and discovered something surprising: The Fee and the Spotlight are actually best friends. In economics, we call them "strategic complements." This means that if you have a high fee, you want to use the spotlight more. And if you use the spotlight more, you want to charge a higher fee. They feed off each other.

The Big Surprise: One Hand Clapping

Because these two tools work together, the paper finds that stopping one of them automatically stops the other.

Imagine the Mall Owner is holding a balloon in each hand. One hand holds the "Fee," the other holds the "Spotlight." If a regulator (like a police officer for the digital world) tells the owner, "Put down the Spotlight!" the owner doesn't just shrug and squeeze the Fee balloon harder. Instead, because the two are linked, the owner naturally lets go of the Fee balloon too.

The paper shows that:

If you ban self-preferencing (force the spotlight to be neutral), the platform will naturally choose to charge a lower fee.
If you cap the fee (force the tax to be low), the platform will naturally choose to use the spotlight less.

This is great news for regulators. It means you don't need to ban everything at once to fix the problem. Tackling just one of these issues is enough to pull the rug out from under the other. The European Union's Digital Markets Act (DMA), which bans self-preferencing, is effective on its own because it forces the platform to lower its fees, too.

The Invisible Harm: Why It Looks Fine But Isn't

Here is the most tricky part of the story. The paper argues that this behavior hurts consumers, but it's very good at hiding the evidence.

Usually, when we think of a monopoly or a bad company, we look for signs like: "Did they drive their rivals out of business?" or "Are there fewer sellers now?" or "Did they lose money to do this?"

But in this digital town square, the harm is sneaky:

No One Gets Fired: The Shopkeepers aren't being kicked out of the mall. If the fee gets too high, some leave, but new ones immediately rush in to take their place. The number of sellers stays roughly the same, and they all make zero profit (just enough to stay in business). So, if you count the number of shops, the market looks perfectly competitive!
No Sacrifice: The owner isn't losing money to hurt the Shopkeepers. In fact, the "tax" they charge the Shopkeepers pays for the owner's own shop. It's a self-financing scheme. The owner doesn't need to "recoup" losses later because they are making money right now.
The Real Damage: The damage is that the prices are higher and there are fewer choices for the consumer, even though the mall looks full and busy. The paper calculates that this setup creates a "deadweight loss"—a fancy way of saying that value is being destroyed, and consumers are paying more than they should, even though the market looks healthy on paper.

The Moving Target: The Ratchet and the Rollercoaster

The paper also looks at what happens over time. It imagines two different scenarios for how the Mall Owner expands their business.

Scenario 1: The Ratchet (The One-Way Street)
Imagine the owner slowly opens new sections of the mall, selling their own products in more and more categories. As they expand, they find that they can charge higher fees because they have more power. Once they expand, they rarely shrink back. The fee goes up, the spotlight gets brighter, and consumer welfare goes down. It's like a ratchet wrench: it only turns one way, tightening the grip on consumers.

Scenario 2: The Rollercoaster (The Chaotic Loop)
In a different scenario, the owner might launch products, then pull them, then launch them again. The paper shows that if the products turn over quickly, the system can get chaotic. The fee and the spotlight might go up and down in a weird, unpredictable cycle, like a rollercoaster that never quite settles. Sometimes the footprints of the Mall Brand grow, sometimes they shrink, and the whole system can spin in a loop forever.

The Bottom Line

So, what does this all mean for the real world?

The Tools are Linked: The fee and the spotlight are not enemies; they are partners. You can't have one without the other.
Regulation Works: If you ban the spotlight, the fee drops. If you cap the fee, the spotlight dims. You don't need to do both to get a result, though doing both is even better.
Don't Be Fooled by the Numbers: Just because a marketplace looks full of sellers and competitive doesn't mean it's good for you. The paper proves that you can have a "competitive-looking" market that is actually hurting consumers through hidden fees and biased search results.

The authors suggest that regulators should focus on the "footprint" (how many categories the platform sells in) rather than just watching the fees. If the platform keeps expanding its own products into new areas, that's the real danger sign. And while the math is complex, the message is simple: In the digital town square, the owner's two favorite tricks work together, and stopping one is the key to saving the town.

Technical Summary: Raising Rivals' Costs on Hybrid Platforms

Problem Statement
Hybrid platforms (e.g., Amazon, JD.com, Coupang) operate marketplaces hosting independent third-party (3P) sellers while simultaneously selling their own first-party (1P) products. These platforms utilize two primary instruments to compete: an ad valorem fee ( $\tau$ ) on 3P revenue and self-preferencing ( $\sigma$ ), which boosts the visibility of 1P products in search and recommendations. Regulators in the US, EU, and Asia have expressed concern that constraining one instrument (e.g., banning self-preferencing via the Digital Markets Act) might cause platforms to intensify the other (e.g., raising fees), potentially rendering single-instrument regulation ineffective. Furthermore, standard antitrust tests often fail to detect harm because the exclusionary mechanism is self-financing (fees generate revenue rather than requiring expenditure) and operates under free entry (sellers are displaced at break-even rather than eliminated).

Methodology
The authors develop a tractable theoretical model featuring a vertically integrated platform and a continuum of symmetric 3P sellers with free entry.

Demand Structure: Consumers choose between a 1P product ( $A$ ), a continuum of 3P products ( $j$ ), and an outside option ($0$) using a logit demand system. Utility depends on intrinsic quality ( $v$ ), price ( $p$ ), and a self-preferencing boost ( $\sigma$ ) for the 1P product.
Cost Structure: 3P sellers face a fixed entry cost ( $F$ ) and pay an ad valorem fee $\tau$ . The 1P product is exempt from $\tau$ . Both 1P and 3P products share a marginal cost $c$ .
Platform Optimization: The platform chooses $\tau$ , $\sigma$ , and the 1P price $p_A$ to maximize profit, which comprises 1P margins and fee revenue from 3P sales, minus the cost of self-preferencing $\psi(\sigma)$ .
Dynamic Extensions: The static model is extended into two dynamic environments:
1. Cumulative Footprint: The platform irreversibly expands its 1P presence across categories of varying sizes, modeling a "transitional ratchet."
2. Turnover Footprint: The active footprint fluctuates as products launch and withdraw, modeled via a logistic map to explore non-monotone and chaotic equilibrium paths.

Key Contributions and Results

Strategic Complementarity of Instruments:
The central finding is that the fee ( $\tau$ ) and self-preferencing ( $\sigma$ ) are strategic complements. The platform's profit function is supermodular in $(\tau, \sigma)$ : a higher fee increases the marginal profitability of self-preferencing, and vice versa.
- Result: A binding fee cap lowers the platform's chosen level of self-preferencing, and a non-discrimination mandate ( $\sigma=0$ ) lowers the platform's chosen fee. This contradicts the "whack-a-mole" fear that constraining one instrument shifts effort to the other.
Mechanism of Consumer Harm:
Under free entry, consumer welfare is pinned down entirely by the fee $\tau$ . Self-preferencing has zero direct effect on consumer surplus ( $W_\sigma = 0$ ) because entry adjusts to restore the inclusive value of the marketplace. However, self-preferencing indirectly lowers welfare by inducing a higher optimal fee.
- Result: The platform's equilibrium fee strictly exceeds the welfare-maximizing level, creating a computable deadweight loss (DWL). The harm is driven by the fee, which raises 3P effective marginal costs and diverts demand to the 1P product.
Failure of Conventional Antitrust Tests:
The conduct achieves the outcomes of monopolization (higher prices, reduced welfare) without the traditional markers.
- No Sacrifice: The exclusionary instrument (the fee) is revenue-generating, not a cost. Thus, there is no "sacrifice" to detect for recoupment screens (e.g., Brooke Group).
- No Elimination: Free entry ensures per-seller profit is zero. Rivals are displaced at break-even, not eliminated.
- Observational Equivalence: Market structure statistics (number of sellers, HHI, per-seller profits) do not identify consumer welfare. Configurations with identical market structures can yield vastly different welfare levels depending on the fee.
Dynamic Implications:
- Transitional Ratchet: In the cumulative expansion model, as the platform enters new categories, the fee rises monotonically with the footprint until a steady state is reached. Welfare declines progressively during this transition.
- Chaos and Cycles: In the turnover model, the interaction between the platform's instruments and the active footprint can generate period-three cycles and chaotic equilibrium paths. This implies that irregular expansion and contraction of the platform's footprint are endogenous outcomes of rational optimization, not necessarily evidence of erratic behavior.
Policy Effectiveness:
Because the instruments are complements, single-instrument regulation is effective.
- A ban on self-preferencing (like EU DMA Article 6(5)) reduces the fee.
- A fee cap reduces self-preferencing.
- Combining both instruments yields weakly better outcomes than either alone. The paper suggests that while self-preferencing bans are effective, adding fee caps is a natural and potent next step.

Significance and Claims
The paper claims to resolve the regulatory uncertainty regarding whether constraining one hybrid platform instrument exacerbates the other. By establishing strategic complementarity, it validates the efficacy of the EU's Digital Markets Act self-preferencing prohibition even in the absence of fee caps.

Furthermore, the paper argues that the hybrid platform model represents a novel form of "raising rivals' costs" that bypasses traditional antitrust screens. Unlike classical cost-raising strategies (Salop and Scheffman, 1983) which require costly outlays to be recouped later, the hybrid platform's exclusion is self-financing. Consequently, the "recoupment" screen is inapplicable, and the "elimination of rivals" screen fails because displacement occurs at break-even under free entry.

The authors conclude that the marketplace can appear competitive to standard structural tests while simultaneously reducing consumer welfare. The primary policy implication is that regulators should focus on the fee structure and the platform's "footprint" (the scope of categories where it sells 1P goods) rather than relying solely on market concentration metrics or looking for evidence of predatory pricing sacrifices.