A note on the non-coincidence of the core and the bargaining set in many-to-one assignment markets
中文摘要
本文分析了一对一指派博弈中关于谈判集、核心与内核之间关系的著名结果在多大程度上能够推广到多对一指派市场, 进而推广到多对多市场。借助一个极小反例, 我们表明谈判集未必与核心重合, 且内核可能不包含在核心之内。我们想强调指出, 如在多对一指派博弈中所观察到的, 核心与谈判集不重合这一现象是相当值得注意的。与其他各类高度结构化的博弈相比时尤其如此, 这些博弈中有许多源自组合优化问题, 例如多对一指派博弈背后所对应的组合优化问题。
Abstract
This paper analyzes the extent to which well-known results on the relationship between the bargaining set, the core, and the kernel in one-to-one assignment games generalize to many-to-one assignment markets, and by extension, many-to-many markets. Using a minimal counterexample, we show that the bargaining set does not necessarily coincide with the core and that the kernel may not be contained within the core. We would like to highlight that the failure of the coincidence between the core and the bargaining set, as observed in the many-to-one assignment game, is quite notable. This is especially true when compared to various other highly structured games, many of which emerge from combinatorial optimization problems, such as the one underlying many-to-one assignment games.