A note on the non-coincidence of the core and the bargaining set in many-to-one assignment markets
通过一个最小反例，证明在多对一指派市场中议价集不一定等于核心，且核可能不包含在核心内，这与一对一情形不同。
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.