Existence of a larger subclass of many-to-one assignment games satisfying the CoMa-property

Investigate whether there exists a subclass of many-to-one assignment games, strictly larger than the class of one-to-one assignment games, in which every extreme core allocation is a marginal payoff vector (the CoMa-property), and characterize such a subclass if it exists.

Background

In one-to-one assignment games, all extreme core allocations are marginal vectors (the CoMa-property). The authors show that this property does not generally hold in many-to-one assignment games, even under dominant diagonal conditions, by providing counterexamples where some extreme core points are not marginal.

The open question seeks to identify whether a broader but still tractable subclass of many-to-one assignment games exists in which the CoMa-property holds, thereby extending structural insights from one-to-one settings and clarifying the boundary between models where marginal-vector characterizations of extreme core points remain valid.