[Paper Review] Optimal Search Segmentation Mechanisms for Online Platform Markets

Zhenzhe Zheng, R. Srikant|arXiv (Cornell University)|Aug 20, 2019

Consumer Market Behavior and Pricing35 references4 citations

TL;DR

This paper studies search segmentation mechanisms on online platforms under the discriminatory control model, where platforms select which sellers to display to buyers. Using a multinomial logit (MNL) model for buyer choice and Bertrand competition for pricing, it proves that social welfare is maximized by displaying all products, while revenue is maximized by showing only sellers above a quality threshold. The optimal thresholds are computable in linear time and exhibit a simple structure across both objectives and competition models (Bertrand and Cournot).

ABSTRACT

Online platforms, such as Airbnb, hotels.com, Amazon, Uber and Lyft, can control and optimize many aspects of product search to improve the efficiency of marketplaces. Here we focus on a common model, called the discriminatory control model, where the platform chooses to display a subset of sellers who sell products at prices determined by the market and a buyer is interested in buying a single product from one of the sellers. Under the commonly-used model for single product selection by a buyer, called the multinomial logit model, and the Bertrand game model for competition among sellers, we show the following result: to maximize social welfare, the optimal strategy for the platform is to display all products; however, to maximize revenue, the optimal strategy is to only display a subset of the products whose qualities are above a certain threshold. We extend our results to Cournot competition model, and show that the optimal search segmentation mechanisms for both social welfare maximization and revenue maximization also have simple threshold structures. The threshold in each case depends on the quality of all products, the platform's objective and seller's competition model, and can be computed in linear time in the number of products.

Motivation & Objective

• To analyze how online platforms can optimize search segmentation to maximize social welfare and revenue under the discriminatory control model.
• To model buyer behavior using the multinomial logit (MNL) choice model and seller competition via Bertrand and Cournot games.
• To derive closed-form expressions for equilibrium social welfare and revenue under endogenous pricing.
• To identify the optimal search segmentation mechanism—i.e., which subset of sellers to display—for both social welfare and revenue maximization.
• To extend results to Cournot competition and show threshold-based mechanisms remain optimal.

Proposed method

• Model buyer choice using the multinomial logit (MNL) model, translating preferences into softmax-based demand functions.
• Formulate seller competition as a Bertrand game with homogeneous product substitutes, deriving a unique pure Nash equilibrium via first-order conditions.
• Express equilibrium social welfare and revenue using a variant of the Lambert W function for analytical tractability.
• Propose a search segmentation mechanism that selects a subset of sellers based on a quality threshold, optimizing platform objectives.
• Prove optimality of threshold-based selection through quasi-convexity analysis of welfare and revenue functions in the context of product substitution.
• Extend results to Cournot competition, showing similar threshold structures emerge for both social welfare and revenue maximization.

Experimental results

Research questions

• RQ1 What is the optimal set of sellers to display to maximize social welfare in a platform market with endogenous pricing?
• RQ2 How should a platform select sellers to display to maximize its own revenue under Bertrand competition and MNL buyer choice?
• RQ3 Does the optimal search segmentation mechanism exhibit a simple threshold structure in both social welfare and revenue maximization?
• RQ4 How do the optimal thresholds depend on product quality, competition model (Bertrand vs. Cournot), and platform objectives?
• RQ5 Can the optimal segmentation be computed efficiently, and what is the computational complexity of identifying the threshold set?

Key findings

• To maximize social welfare, the optimal platform strategy is to display all available products, as any subset selection reduces total surplus.
• To maximize revenue, the optimal strategy is to display only sellers whose quality exceeds a specific threshold, which depends on the full set of product qualities and the competition model.
• The optimal threshold for revenue maximization is computable in linear time relative to the number of products, enabling efficient implementation.
• The optimal search segmentation mechanism for both social welfare and revenue maximization under Bertrand competition has a clean threshold structure based on product quality.
• The results extend to Cournot competition, where similar threshold-based mechanisms are optimal for both objectives, with thresholds dependent on the same factors.
• The proof relies on showing that the welfare and revenue functions are quasi-convex in the replacement of lower-quality with higher-quality products, ensuring optimality of top-quality subsets.