(Submodular) Hedonic Games with Common Ranking Property

We study hedonic games with common ranking property (HGCRP), where all members of a coalition receive the same utility. We prove the existence of partitions that are both strong individually stable (SIS) and Pareto optimal (PO), as well as partitions that are contractually Nash stable (CNS) and PO. Moreover, we show that an SIS partition can be found in polynomial time. We introduce a subclass of HGCRP with submodular joint utility functions and establish that its stability and efficiency properties align with those of general HGCRP. Finally, we show that the core price of anarchy and stability in submodular HGCRP are both n, where n is the number of agents.

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