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

The Hidden Synergy of Hybrid Platforms

Large online marketplaces that sell their own products alongside third-party sellers use two powerful tools: charging high fees and making their own products more visible. Regulators have long worried that if they restrict one of these behaviors, the platform will simply pivot to the other. This creates a game of regulatory "whack-a-mole." A new study from researchers at Montclair State University suggests this fear might be misplaced.

The authors report that these two instruments—fees and self-preferencing—actually work in tandem. Rather than acting as substitutes, they are strategic complements. This means that constraining one tool naturally curbs the effectiveness of the other. Consequently, single-instrument regulations could be more powerful than previously thought.

The Mechanics of Dual-Mode Retail

The core issue involves "hybrid platforms." These are marketplaces that host independent third-party (3P) sellers while simultaneously selling their own first-party (1P) goods. Think of a shopping mall that rents out storefronts to local boutiques but also operates its own flagship department store in the center.

The platform exerts influence through two primary levers. First, it sets an ad valorem fee ($\tau$), which is a percentage commission taken from every sale made by a third party. This fee effectively raises the cost of doing business for rivals. Second, it employs self-preferencing ($\sigma$), the intentional boosting of its own 1P products in search rankings or recommendation widgets.

The central tension is whether these two levers are independent or linked. If they are substitutes, a regulator banning self-preferencing might just trigger a massive hike in merchant fees. However, the study finds the instruments are strategic complements. This relationship is driven by supermodularity (a mathematical property where the marginal benefit of one variable increases as another variable increases).

The Logic of Strategic Complements

To investigate this, the authors developed a theoretical model using a logit demand system. This is a mathematical framework used to model how consumers choose between discrete options based on relative utility. The model assumes a continuum of 3P sellers who face a fixed entry cost ($F$).

The study finds that the platform's profit is supermodular in fees and self-preferencing. Specifically, the authors report that a higher fee makes the platform more incentivized to self-preference. Similarly, more self-preferencing makes the fee more profitable.

This relationship leads to several striking conclusions. First, the authors demonstrate that the platform's optimal 1P price ($p_A$) is always exactly the fee amount higher than the 3P price ($p_S$): $p_A - p_S = \tau$. Second, they find that self-preferencing has no direct impact on consumer surplus ($W_\sigma = 0$) under conditions of free entry. Instead, it hurts consumers indirectly by driving the platform to set even higher fees.

The researchers also highlight a "displacement" effect. Because the model assumes free entry, third-party sellers aren't necessarily driven into bankruptcy. Instead, the high fees simply reduce the total number of sellers that can afford to stay in a category. As seen in [Figure 1b], the number of active sellers ($N_S$) can remain constant across different combinations of fees and entry costs. Even so, consumer welfare can fluctuate wildly during these shifts.

Why Traditional Antitrust Tests Fail

One of the most significant findings is that this dual-strategy can mimic a monopoly. It can do this while appearing perfectly competitive to standard regulators. Conventional antitrust scrutiny often looks for "sacrifice"—evidence that a firm is losing money to kill a rival. It also looks for sudden spikes in market concentration.

The authors report that this platform behavior bypasses those screens. Because the fee is a revenue stream rather than an expense, the exclusion is "self-financing." There is no upfront cost for the platform to recoup. Furthermore, because new sellers constantly enter the market to replace those displaced by fees, the number of competitors may not show typical red flags.

This creates a disconnect between market structure and consumer harm. As illustrated in [Figure 1b], a regulator looking only at the number of sellers ($N_S$) might conclude a market is healthy. However, the combination of fees and visibility boosts is actively eroding consumer welfare.

The study also explores how this behavior evolves over time. In a "transitional ratchet" scenario, as a platform expands its footprint into new product categories, the fee tends to rise monotonically [Figure 1a]. Conversely, in environments with high product turnover, the authors find that the platform's footprint, fees, and welfare can enter periodic cycles or even chaotic, unpredictable paths.

Where the Framework Breaks

While the model provides a robust lens for viewing platform power, it relies on specific assumptions. Most notably, the results hinge on the assumption of "free entry." This assumes sellers can join the marketplace with minimal friction. If sellers face significant sunk costs—investments that cannot be recovered if they leave—the "displacement" mechanism changes. In that case, the platform's conduct might look more like traditional predatory pricing.

Additionally, the authors note that the zero direct effect of self-preferencing on consumer surplus is tied to the use of logit demand. While the principle of strategic complementarity likely persists in other models, the exact mathematical relationship might vary. Finally, the model assumes symmetric marginal costs between the platform's own goods and those of its rivals. If the platform has significantly different cost structures, the pricing gaps would shift accordingly.

Figures from the paper