Stable Matching with Deviators and Conformists

2026-01-26

AI Summary

This study addresses a novel model in stable matching where agents are partitioned into deviators—those who may strategically deviate from prescribed behavior—and conformists, who adhere strictly to the matching protocol. The work formally introduces this deviator-conformist framework and investigates the existence of matchings that are either free of deviator-blocking pairs or admit only a bounded number of such blocks. Through rigorous computational complexity analysis and problem reductions, the authors establish that the general problem is NP-complete, thereby extending beyond the tractability boundary of classical stable matching. Nevertheless, they identify several special cases that are solvable in polynomial time or fixed-parameter tractable, offering new algorithmic foundations for designing matching mechanisms in multi-agent systems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the celebrated Gale-Shapley algorithm, the existence of a stable matching is not guaranteed in the latter problem, but can be determined efficiently using Irving's algorithm. However, the computation of matchings that minimise the instability, either due to the presence of additional constraints on the size of the matching or due to restrictive preference cycles, gives rise to a collection of infamously intractable almost-stable matching problems. In practice, however, not every agent is able or likely to initiate deviations caused by blocking pairs. Suppose we knew, for example, due to a set of requirements or estimates based on historical data, which agents are likely to initiate deviations - the deviators - and which are likely to comply with whatever matching they are presented with - the conformists. Can we decide efficiently whether a matching exists in which no deviator is blocking, i.e., in which no deviator has an incentive to initiate a deviation? Furthermore, can we find matchings in which only a few deviators are blocking? We characterise the computational complexity of this question in bipartite and non-bipartite preference settings. Surprisingly, these problems prove computationally intractable in strong ways: for example, unlike in the classical setting, where every agent is considered a deviator, in this extension, we prove that it is NP-complete to decide whether a matching exists where no deviator is blocking. On the positive side, we identify polynomial-time and fixed-parameter tractable cases, providing novel algorithmics for multi-agent systems where stability cannot be fully guaranteed.

Problem

• Stable Matching
• Deviators
• Conformists
• Blocking Pairs
• Computational Complexity

Innovation

• stable matching
• deviators and conformists
• computational complexity
• blocking pairs
• fixed-parameter tractability