Strict Core Stability and Strategy-Proofness for Hedonic Games with Friend-Oriented Preferences
summary
Shows that the SCC partition of the directed friendship graph is always in the strict core for friend-oriented hedonic games, and the mechanism that outputs those strongly connected components is polynomial-time computable, strictly core-stable and satisfies group strategy-proofness (proved via condensation-graph induction). Main uniqueness claim: on any rich subdomain where any friend set can be reported, the SCC mechanism is the only core-stable and strategy-proof rule. Adding neutrals can empty the strict core and breaks full group-proofness, but preserves weak-group guarantees.
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