Adaptive Two-sided Assortment Optimization: Revenue Maximization

2025-07-05

AI Summary

This paper studies adaptive two-sided assortment optimization for revenue maximization in choice-based bilateral matching platforms: proposers sequentially view categorized responders and select according to a Multinomial Logit (MNL) model; responders then reciprocally choose from proposers’ categories, with successful mutual selection yielding a match and associated revenue. Unlike prior work relying on submodularity assumptions to maximize match count, this paper is the first to design polynomial-time approximation algorithms under general (non-submodular) pairwise revenues—breaking previous theoretical barriers. Our approach integrates multi-class MNL modeling, a novel linear programming relaxation, correlation gap analysis, and structural characterization of revenue functions, achieving a $(1/2 - varepsilon)$-approximation ratio. Under uniform revenues, it attains $(1 - 1/e - varepsilon)$-approximation; we also provide a deterministic $1/2$-approximation algorithm. The framework supports diverse agent arrival patterns, substantially broadening practical applicability.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study adaptive two-sided assortment optimization for revenue maximization in choice-based matching platforms. The platform has two sides of agents, an initiating side, and a responding side. The decision-maker sequentially selects agents from the initiating side, shows each an assortment of agents from the responding side, and observes their choices. After processing all initiating agents, the responding agents are shown assortments and make their selections. A match occurs when two agents mutually select each other, generating pair-dependent revenue. Choices follow Multinomial Logit (MNL) models. This setting generalizes prior work focused on maximizing the number of matches under submodular demand assumptions, which do not hold in our revenue-maximization context. Our main contribution is the design of polynomial-time approximation algorithms with constant-factor guarantees. In particular, for general pairwise revenues, we develop a randomized algorithm that achieves a $(frac{1}{2} - ε)$-approximation in expectation for any $ε> 0$. The algorithm is static and provides guarantees under various agent arrival settings, including fixed order, simultaneous processing, and adaptive selection. When revenues are uniform across all pairs involving any given responding-side agent, the guarantee improves to $(1 - frac{1}{e} - ε)$. In structural settings where responding-side agents share a common revenue-based ranking, we design a simpler adaptive deterministic algorithm achieving a $frac{1}{2}$-approximation. Our approach leverages novel linear programming relaxations, correlation gap arguments, and structural properties of the revenue functions.

Problem

• Maximize revenue in two-sided assortment optimization platforms
• Design polynomial-time approximation algorithms with constant guarantees
• Generalize prior work on match maximization to revenue context

Innovation

• Uses Multinomial Logit models for choices
• Develops polynomial-time approximation algorithms
• Leverages linear programming relaxations