Matching Markets with Pre-Existing Binding Agreements: Analyzing Outcomes in the Agreeable Core

Core Concepts

This paper introduces the "agreeable core" as a solution concept for matching markets where participants may have pre-existing binding agreements, and presents the Propose-Exchange algorithm, a novel method combining elements of Deferred Acceptance and Top Trading Cycles algorithms, to find a stable and agreeable matching outcome.

Abstract

• Bibliographic Information: Doe, P. (2024). Matching With Pre-Existing Binding Agreements: The Agreeable Core. arXiv preprint arXiv:2406.08700v2.
• Research Objective: To address the limitations of traditional matching models in scenarios with pre-existing agreements by introducing a new solution concept called the "agreeable core" and proposing an algorithm to find such solutions.
• Methodology: The paper develops a theoretical framework using graph theory to represent matching problems with pre-existing agreements. It then introduces the concept of "agreeable coalitions" and defines the "agreeable core" based on these coalitions. Finally, it proposes the Propose-Exchange algorithm, a two-stage algorithm combining elements of Deferred Acceptance and Top Trading Cycles, to find a match within the agreeable core.
• Key Findings: The paper demonstrates that the agreeable core is always non-empty and provides a method for finding a stable matching outcome that respects pre-existing agreements. The Propose-Exchange algorithm is presented as an efficient way to reach such an outcome.
• Main Conclusions: The agreeable core offers a more realistic and applicable solution concept for matching markets with pre-existing binding agreements, which are common in real-world scenarios like job markets and school choice programs. The Propose-Exchange algorithm provides a practical method for implementing this solution concept.
• Significance: This research contributes significantly to matching theory by addressing a key limitation of traditional models and offering a practical solution for handling pre-existing agreements. This has implications for various real-world matching markets.
• Limitations and Future Research: The paper primarily focuses on one-to-one matching scenarios. Further research could explore extending the agreeable core and the Propose-Exchange algorithm to many-to-one matching problems. Additionally, investigating the strategic properties of the Propose-Exchange algorithm in more detail would be beneficial.

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Matching With Pre-Existing Binding Agreements: The Agreeable Core

by Peter Doe at arxiv.org 11-04-2024

https://arxiv.org/pdf/2406.08700.pdf

Deeper Inquiries

How can the concept of the "agreeable core" be applied to improve the design of online platforms for freelance work, where individuals often have ongoing commitments?

The "agreeable core" presents a novel approach to handle pre-existing commitments in matching markets, making it highly relevant to online freelance platforms. Here's how it can be applied:
1. Integrating Ongoing Projects:

Identifying Agreeable Coalitions: Platforms can use the concept of "agreeable coalitions" to identify freelancers and clients who can renegotiate contracts without jeopardizing existing commitments. For instance, a freelancer with an ongoing project can only be part of a coalition that includes their current client.
Facilitating Contract Renegotiation: The platform can provide tools that allow agreeable coalitions to renegotiate terms, deadlines, or even swap projects, ensuring all parties involved benefit from the new arrangement.
2. Prioritizing Availability and Transparency:

Displaying Commitment Levels: Platforms can incorporate a system that clearly displays the commitment level of each freelancer (e.g., partially available, fully booked). This transparency helps clients understand potential limitations upfront.
Prioritizing Matching within Agreeable Groups: The platform's algorithm can prioritize matching clients with freelancers who are either fully available or belong to agreeable coalitions where the client's project fits within existing commitments.
3. Enhancing Trust and Reducing Market Congestion:

Reducing Reneging and Last-Minute Cancellations: By ensuring that contract modifications only occur within agreeable coalitions, the platform minimizes the risk of freelancers reneging on commitments due to more favorable offers.
Improving Matching Efficiency: The focus on agreeable coalitions streamlines the matching process. Clients are more likely to find suitable freelancers who are genuinely available, reducing time wasted on negotiations that are unlikely to materialize.
Example:
Imagine a freelance platform for web developers. A client needs a website redesign but has a tight deadline. The platform identifies an agreeable coalition consisting of:

Client A: Needs a website redesign (high urgency).
Freelancer B: Committed to a long-term project with Client C but has some availability.
Client C: Has a less urgent task that can be postponed.
The platform facilitates a renegotiation within this coalition. Freelancer B can take on the website redesign by slightly delaying Client C's project. All parties agree, ensuring a mutually beneficial outcome.
By incorporating the principles of the agreeable core, freelance platforms can create a more efficient and reliable marketplace that respects existing commitments while allowing for flexibility and mutually beneficial contract adjustments.

Could there be alternative solution concepts beyond the "agreeable core" that might be more suitable in situations where pre-existing agreements carry different levels of weight or enforceability?

While the "agreeable core" provides a robust framework for handling binding pre-existing agreements, real-world scenarios often involve agreements with varying degrees of formality and enforceability. Here are some alternative solution concepts:
1. Weighted Agreeable Core:

Assigning Weights to Agreements: Instead of treating all agreements as equally binding, assign weights based on factors like contract value, duration, or penalty for breach.
Modifying Blocking Power: A coalition's ability to block a proposed match would depend on the combined weight of the agreements it's willing to dissolve. Coalitions with higher combined weights would have more blocking power.
2. Flexible Agreement States:

Introducing Agreement States: Move beyond a binary "binding" or "non-binding" state. Agreements could have states like "flexible," "negotiable," or "strict," reflecting the willingness of parties to renegotiate.
Dynamic Matching Process: The matching algorithm could prioritize matches that require minimal disruption of "strict" agreements while allowing more flexibility for "negotiable" or "flexible" ones.
3. Reputation and Penalty Systems:

Quantifying Agreement Reliability: Develop a reputation system that reflects an agent's history of honoring commitments. Agents with poor reputations might face higher barriers to joining desirable coalitions.
Penalty for Breach: Implement a system of penalties for breaching agreements. The severity of the penalty could be tied to the agreement's weight or enforceability level.
4. Hybrid Approaches:

Combining Core Concepts: Combine elements of the agreeable core with other matching concepts like stability or fairness metrics. For instance, prioritize matches within the agreeable core that also minimize envy or maximize overall welfare.
Example:
Consider a platform for booking musicians for events. A musician might have:

A Signed Contract (Strict): A legally binding contract for a wedding with a high penalty for cancellation.
A Verbal Agreement (Negotiable): A less formal agreement to play at a bar, where renegotiation is possible.
An Open Slot (Flexible): A completely free slot open to any offer.
The platform's algorithm would prioritize fulfilling the "strict" contract, explore renegotiation options for the "negotiable" agreement, and consider the "flexible" slot for any suitable match.
By incorporating these alternative solution concepts, matching platforms can better adapt to the complexities of real-world agreements, balancing the need to honor commitments with the flexibility to accommodate mutually beneficial arrangements.

What are the ethical implications of using algorithms like the Propose-Exchange in matching markets, particularly concerning fairness and potential biases in the initial match or preference data?

While algorithms like the Propose-Exchange offer a structured approach to navigating complex matching scenarios with pre-existing agreements, their ethical implications, particularly regarding fairness and bias, require careful consideration.
1. Amplifying Existing Biases:

Initial Match Bias: If the initial match (µ0) itself reflects existing societal biases (e.g., discrimination based on gender, race, or socioeconomic background), the Propose-Exchange algorithm, while aiming for Pareto efficiency, might perpetuate and even exacerbate these biases. The algorithm operates under the constraint of individual rationality with respect to µ0, meaning it might not undo unfair initial pairings.
Preference Data Bias: The algorithm relies on preference data from both sides of the market. If this data contains biases (e.g., clients unconsciously favoring certain demographics), the algorithm can learn and reinforce these biases, leading to discriminatory outcomes.
2. Transparency and Explainability:

Black Box Effect: The Propose-Exchange algorithm, especially as it scales, can become complex and opaque. This lack of transparency makes it difficult for participants to understand why they were matched with a particular partner or why a proposed renegotiation was accepted or rejected.
Erosion of Trust: Opacity in algorithmic decision-making can erode trust in the platform. Participants might perceive the system as unfair or arbitrary, especially if they cannot comprehend the rationale behind the outcomes.
3. Fairness Considerations:

Unequal Bargaining Power: Even within agreeable coalitions, the algorithm doesn't inherently address potential power imbalances. For instance, a freelancer in high demand might have more leverage to dictate terms during renegotiations, potentially disadvantaging other parties within the coalition.
Distributional Fairness: While the agreeable core aims for Pareto efficiency, it doesn't guarantee fairness in the distribution of benefits. Some participants, especially those starting with advantageous positions in the initial match, might consistently benefit more than others.
Mitigating Ethical Concerns:

Auditing and Bias Detection: Regularly audit the algorithm and the underlying data for biases. Implement bias mitigation techniques during data collection, pre-processing, and within the algorithm itself.
Transparency and Explainability: Strive for transparency by providing participants with clear explanations of how the algorithm works and the factors influencing their matches. Offer insights into how renegotiations within agreeable coalitions are evaluated.
Fairness Constraints: Incorporate fairness constraints directly into the algorithm's objective function. For example, prioritize matches that promote diversity or ensure a more equitable distribution of benefits among participants.
Human Oversight and Appeal Mechanisms: Maintain human oversight in critical aspects of the matching process, especially when resolving disputes or handling cases that fall outside the algorithm's parameters. Provide accessible appeal mechanisms for participants who believe they've been treated unfairly.
By acknowledging and proactively addressing these ethical implications, designers of matching platforms can work towards creating systems that are not only efficient but also fair, transparent, and accountable.