Pseudo-Substitutability: A Maximal Domain for Pairwise Stability in Matching Markets with Contracts

2026-04-20

AI Summary

This study addresses the limitations of classical substitutable preferences in matching markets, which are too restrictive to capture limited complementarities among contracts. The paper introduces a broader preference domain—“pseudo-substitutable preferences”—that accommodates such complementarities while still guaranteeing the existence of pairwise stable allocations. This new domain strictly encompasses traditional substitutable preferences and is shown to be maximal with respect to the existence of stable matchings. By leveraging tools from matching theory and mechanism design, the work not only establishes the existence of stable allocations under pseudo-substitutability but also precisely characterizes the boundary of preference domains compatible with stability, thereby overcoming the constraints imposed by conventional assumptions.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We study the existence of pairwise stable allocations in matching markets with contracts and propose a domain restriction that guarantees their existence. Specifically, we define pseudo-substitutable preferences, a domain that strictly extends the classical notion of substitutability while still preserving the existence of pairwise stable allocations. This domain accommodates limited complementarities among contracts while retaining enough structure to preserve the key stability properties of substitutable preferences. Moreover, we show that, among all preference domains that contain the classical substitutable domain and guarantee the existence of pairwise stable allocations, the pseudo-substitutable domain is maximal. Our results establish that pairwise stability extends well beyond the classical substitutable domain.

Problem

• matching markets
• contracts
• pairwise stability
• substitutability
• pseudo-substitutability

Innovation

• pseudo-substitutability
• pairwise stability
• matching markets with contracts
• substitutable preferences
• maximal domain