Designing Pairwise-Stable Agent Seating Arrangements

2026-07-29

AI Summary

This work addresses the limitations of traditional multi-agent stable matching approaches, which assume a fixed underlying graph structure and often yield no solution or become computationally intractable. Departing from this assumption, the paper treats the graph structure itself as a design variable and introduces a unified framework that jointly optimizes graph design and matching under ordinal agent preferences. By integrating concepts from stable matching theory, graph design, subgraph isomorphism, and combinatorial optimization, the framework efficiently constructs near-optimal, pairwise-stable configurations, substantially broadening the applicability of stable matching. The study delineates the boundary of solvability, enables efficient stable arrangements on a wider class of graph topologies beyond simple paths and cycles, and uncovers an intrinsic trade-off between stability guarantees and computational complexity.

Abstract

Many fundamental problems in multi-agent systems involve the arrangement of agents, who have preferences over each other, on a target graph. These problems include, for example, Stable Matching, Seat Arrangement, and Coalition Formation. However, guaranteeing game-theoretically desirable properties such as exchange-stability or envy-freeness is difficult, as such solutions may not exist, and even if they do, they are often intractable to find, even in highly constrained settings such as path or cycle target graphs. In this paper, we challenge the classical setup and investigate what can be achieved when the structure of the target graph is a designable object for the central planner, rather than a fixed part of the input. We study this in the context of a natural pairwise stability criterion, which is similar to having spare seats. In particular, we introduce a highly flexible framework to efficiently design approximately optimal target graphs and associated pairwise-stable agent arrangements. Our model assumes that agents have (weak or strict) ordinal preferences over other agents. We show that classical results from stable matching theory can be extended and adapted to this much more general setting and can serve as a useful tool for navigating the trade-off between stability and computational efficiency. Our results highlight strict boundaries between tractability and intractability, and between local and global optimality. We also uncover intriguing connections to classical computational problems such as subgraph isomorphism, disjoint path partitioning, and bin-packing.

Problem

• pairwise stability
• agent seating arrangement
• target graph design
• multi-agent systems
• ordinal preferences

Innovation

• pairwise stability
• graph design
• stable matching
• multi-agent arrangement
• computational tractability