Price Stability and Improved Buyer Utility with Presentation Design: A Theoretical Study of the Amazon Buy Box

TL;DR

The paper investigates how platform-driven prominence, exemplified by the Amazon Buy Box, affects pricing equilibria in a monopolistic-competition setting with search frictions. By modeling buyer search via Pandora’s Box and introducing prominence mechanisms (dictator and threshold), it shows that plain price presentation lacks pure equilibria, while carefully designed prominence can stabilize prices and yield well-defined implementable price intervals. It analyzes welfare and consumer surplus, revealing that higher search friction can boost buyer surplus under certain distributions and parameter regimes. The findings offer theoretical guidance for platform design, showing that visibility controls can shape competition and welfare in online marketplaces.

Abstract

Platforms design the form of presentation by which sellers are shown to the buyers. This design not only shapes the buyers' experience but also leads to different market equilibria or dynamics. One component in this design is through the platform's mediation of the search frictions experienced by the buyers for different sellers. We take a model of monopolistic competition and show that, on one hand, when all sellers have the same inspection costs, the market sees no stable price since the sellers always have incentives to undercut each other, and, on the other hand, the platform may stabilize the price by giving prominence to one seller chosen by a carefully designed mechanism. This calls to mind Amazon's Buy Box. We study natural mechanisms for choosing the prominent seller, characterize the range of equilibrium prices implementable by them, and find that in certain scenarios the buyers' surplus improves as the search friction increases.

Figures (4)

• Figure 1: Illustration of Amazon's Buy Box. Top: The Buy Box is highlighted in red. To view other sellers not in the Buy Box, a buyer needs to scroll down and click on the link we highlight in green. Bottom: A view of sellers not in the Buy Box.
• Figure 2: Illustration for a step in the proof of Theorem \ref{['theorem:no_BB_no_eq']}. The equilibrium conditions, together with Lemma \ref{['lemma:all_buy']}, require that seller 1's demand, as the seller varies their price, is sandwiched between an upper bound $g_1$ and a lower bound $g_2$, all three functions expressed in a common variable $\Delta'_p$. They coincide at the point $\Delta'_p = \Delta_p$, which is the hypothetical equilibrium point. The three functions must have the same derivative at $\Delta'_p = \Delta_p$.
• Figure 3: Illustration of implementable prices with threshold mechanisms. For two sellers, with $F$ supported on $[2, 3]$ and pdf proportional to $e^{v - 2}$, the magenta area illustrates the range of prices implementable with the threshold mechanism as the inspection cost $c$ varies. The blue area is the range of prices implementable with the dictator mechanism but not with the threshold mechanism.
• Figure 4: Illustration of feasible consumer surplus and seller revenue at equilibrium, colored with corresponding inspection cost. We plot the region of feasible consumer surplus vs. seller revenues (for two sellers with $F = U[2, 3]$) at equilibrium, and color the region with corresponding inspection cost that admits the equilibrium. The Pareto Frontier is achieved when prices are lowest at $t^*(c)$, where the consumer surplus is maximized.

Theorems & Definitions (64)

• Lemma 1: kleinberg2016descending
• Proposition 1
• proof
• Proposition 2
• Theorem 1
• Lemma 2
• Theorem 2
• Definition 1
• Definition 2
• Proposition 3