Quasi-Stability Notions in Two-Sided Matching Markets: Exploring Worker and Firm Preferences

核心概念

This paper introduces new quasi-stability concepts for matching markets, specifically worker-quasi-core, firm-quasi-core, worker-quasi-setwise stable, and firm-quasi-setwise stable matchings, to analyze stability in scenarios where agents have multiple, substitutable partners.

摘要

Bibliographic Information:

Guiñazú, N., Juarez, N., Neme, P., & Oviedo, J. (2024). Quasi-stability notions in two-sided matching models. arXiv preprint arXiv:2411.12533v1.

Research Objective:

This paper aims to introduce and analyze new quasi-stability concepts in two-sided matching markets, extending existing notions to encompass corewise and setwise stability, particularly in scenarios where agents have substitutable preferences.

Methodology:

The authors utilize theoretical analysis and mathematical modeling within the framework of cooperative game theory to define and explore the properties of worker-quasi-core, firm-quasi-core, worker-quasi-setwise stable, and firm-quasi-setwise stable matchings. They examine these concepts in both many-to-one and many-to-many matching market models.

Key Findings:

• In many-to-one markets, the authors establish that individually rational matchings within the worker-quasi-core are equivalent to worker-quasi-stable matchings. Similarly, they demonstrate that individually rational matchings within the firm-quasi-core correspond to firm-quasi-stable matchings.
• However, these characterizations do not directly extend to many-to-many markets due to the added complexity of multiple employment relationships.
• The paper shows that worker-quasi-stable matchings are a subset of the worker-quasi-core in many-to-many markets, but this inclusion can be strict depending on the specific market structure.
• The authors characterize the worker-quasi-setwise stable set using worker-quasi-stable matchings.
• They also demonstrate that a matching exhibiting both worker-quasi-stability and firm-quasi-stability is either pairwise stable or dominated by another matching through a coalition.

Main Conclusions:

The introduction of these new quasi-stability concepts provides a more flexible framework for understanding stability in matching markets, particularly in situations where traditional pairwise stability might be unrealistic or unattainable. These concepts bridge the gap between traditional core-based solutions and quasi-stable structures, offering valuable insights into the dynamics of labor markets and other matching scenarios.

Significance:

This research significantly contributes to the field of matching theory by expanding the understanding of stability beyond traditional concepts. The new quasi-stability notions offer a more nuanced and realistic approach to analyzing stability in complex matching markets, with potential applications in labor economics, market design, and other related fields.

Limitations and Future Research:

The paper primarily focuses on theoretical analysis and characterization of the new quasi-stability concepts. Future research could explore algorithmic aspects, such as developing efficient algorithms for finding these quasi-stable matchings in different market settings. Additionally, empirical studies could investigate the prevalence and characteristics of these quasi-stable matchings in real-world matching markets.

统计

引用

从中提取的关键见解

Quasi-stability notions in two-sided matching models

by Nadi... 在 arxiv.org 11-20-2024

https://arxiv.org/pdf/2411.12533.pdf

更深入的查询

How can these new quasi-stability concepts be applied to other matching markets beyond labor markets, such as education or housing markets?

These quasi-stability concepts, focusing on worker-quasi-core, firm-quasi-core, worker-quasi-setwise stability, and firm-quasi-setwise stability, can be effectively applied to various matching markets beyond labor markets. Here's how:
1. Education Markets:

Student-School Matching: In school choice systems, worker-quasi-stability can model situations where students (workers) prioritize staying at their current school while aiming for better options. A student might not leave their current school for a slightly better alternative unless guaranteed a spot in a significantly more preferable school. This aligns with the concept of allowing blocking pairs only when students are initially unmatched.
School-Faculty Matching: Firm-quasi-stability becomes relevant when schools (firms) prefer to retain their existing faculty while seeking to fill additional positions. Schools are less likely to dismiss current teachers to accommodate new hires, reflecting the constraint of maintaining existing contracts.
2. Housing Markets:

Tenant-Landlord Matching: Worker-quasi-stability can represent tenants (workers) who prioritize securing a new lease before giving up their current housing. Tenants might only move for significantly better housing options due to the costs and inconvenience associated with relocation.
Landlord-Tenant Matching: Firm-quasi-stability can model landlords (firms) who prefer to keep existing tenants while seeking to fill vacancies. Evicting tenants can be costly and time-consuming, making landlords more inclined towards stability.
Key Considerations for Application:

Market Dynamics: The specific application of these concepts requires careful consideration of the market's dynamics. For instance, the relative bargaining power of students and schools in an education market will influence how these quasi-stability notions manifest.
Policy Implications: Understanding these quasi-stability concepts can inform policy decisions in matching markets. For example, in housing markets, policies promoting tenant stability might be designed based on the principles of worker-quasi-stability.

Could there be situations where prioritizing worker-quasi-stability or firm-quasi-stability might lead to less desirable outcomes for the market as a whole?

Yes, prioritizing one side's quasi-stability, either worker-quasi-stability or firm-quasi-stability, can potentially lead to less desirable outcomes for the market as a whole. Here's why:
1. Reduced Market Efficiency:

Worker-Quasi-Stability: Prioritizing worker-quasi-stability might hinder efficient matching. If workers are reluctant to switch jobs even for significantly better offers due to the guaranteed stability of their current positions, it can lead to underemployment of highly skilled workers and limit productivity gains for firms.
Firm-Quasi-Stability: Similarly, prioritizing firm-quasi-stability might discourage firms from hiring more suitable candidates, even if it means replacing existing employees. This can lead to a less dynamic labor market with reduced innovation and growth.
2. Inequality and Fairness Concerns:

Worker-Quasi-Stability: While seemingly beneficial for workers, excessive emphasis on worker-quasi-stability might disproportionately benefit those already employed, potentially creating barriers for newcomers or those seeking re-entry into the market.
Firm-Quasi-Stability: Prioritizing firm-quasi-stability might give firms an unfair advantage in the matching process. This could lead to situations where firms exploit their position, offering less competitive wages or benefits, knowing that workers prioritize job security.
3. Reduced Market Flexibility:

Both Worker and Firm Quasi-Stability: Overemphasizing either form of quasi-stability can reduce the market's ability to adapt to changing conditions. In dynamic markets with evolving skill demands or economic fluctuations, this rigidity can hinder overall market performance.
Balancing Act:
The key takeaway is that achieving a desirable market outcome requires a balanced approach. While quasi-stability concepts offer valuable insights into real-world matching scenarios, policymakers and market designers need to carefully consider the potential trade-offs and strive for solutions that promote both efficiency and fairness.

If we consider the dynamics of a matching market over time, how might these quasi-stability concepts evolve and influence the long-term stability of the market?

Considering the dynamic nature of matching markets, these quasi-stability concepts can significantly influence long-term stability, leading to both positive and negative consequences:
Positive Influences:

Reduced Short-Term Volatility: By allowing for limited deviations, quasi-stability can dampen short-term fluctuations in the market. For instance, in a labor market with worker-quasi-stability, workers are less likely to make frequent job changes for marginal gains, leading to a more predictable and stable workforce.
Reputation and Trust Building: Quasi-stability can foster trust between agents. In a housing market with firm-quasi-stability, tenants might be more inclined to stay with a landlord known for long-term leases, leading to more stable tenant-landlord relationships.
Path Dependency: Initial quasi-stable matchings can influence the market's trajectory. For example, in an education market, if a school develops a reputation for retaining faculty (firm-quasi-stability), it might attract higher-quality applicants in the future, further reinforcing its stability.
Negative Influences:

Stagnation and Inertia: While reducing short-term volatility, prolonged emphasis on quasi-stability can lead to stagnation. If workers and firms prioritize existing matches over potentially better alternatives, it can hinder innovation and productivity growth in the long run.
Inequality Amplification: Over time, quasi-stability might exacerbate existing inequalities. In a labor market with worker-quasi-stability, those initially holding advantageous positions might retain them, while newcomers or those with less bargaining power face greater challenges in securing desirable positions.
Adaptability Challenges: Markets with entrenched quasi-stability might struggle to adapt to external shocks or evolving preferences. For instance, a sudden shift in demand for specific skills in a labor market with strong worker-quasi-stability might lead to a mismatch between skills and job requirements.
Dynamic Perspective is Crucial:
Understanding the dynamic implications of quasi-stability is essential for designing effective matching mechanisms and policies. A static view might overlook the potential long-term consequences of prioritizing one form of stability over another. A balanced approach that considers both the short-term benefits and long-term implications of quasi-stability is crucial for fostering a healthy and adaptable matching market.