设计成对稳定的智能体座位安排
Designing Pairwise-Stable Agent Seating Arrangements
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中文总结 AI 辅助
该研究针对多智能体系统的座位安排问题，将目标图设为可设计对象，提出灵活框架设计近似最优目标图及成对稳定安排，明确了易处理性等界限并关联经典计算问题。
中文摘要 AI 辅助
多智能体系统中的许多基础问题涉及智能体的安排，这些智能体对彼此具有偏好，需被布置在目标图上。这类问题包括稳定匹配、座位安排和联盟形成等。然而，保证博弈论上理想的性质（如交换稳定性或无 envy）十分困难，因为这类解可能不存在，即便存在，也往往难以找到，即使在路径或环等高度受限的目标图设置中亦是如此。本文中，我们对经典设定提出挑战，研究当目标图的结构由中央规划者可设计的对象而非输入的固定部分时，能实现什么。我们在类似有备用座位的自然成对稳定性准则背景下研究这一问题。具体而言，我们引入一个高度灵活的框架，用于高效设计近似最优的目标图及相关的成对稳定智能体安排。我们的模型假设智能体对其他智能体具有弱或严格的序数偏好。我们证明，稳定匹配理论的经典结果可扩展并适配到这个更一般的设置中，且可作为在稳定性与计算效率间权衡的有用工具。我们的结果凸显了易处理性与难处理性、局部最优性与全局最优性之间的严格界限，还揭示了与子图同构、不相交路径划分和装箱等经典计算问题的有趣联系。
英文摘要
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.
