Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
We consider general allocation problems with indivisibilities where agents' preferences possibly exhibit externalities. In such contexts many different core notions were proposed. One is the individually-rational-core (IR-core) whereby blocking is only allowed via allocations where the non-blocking agents receive their endowments. We show that if there exists an allocation rule satisfying individual rationality, efficiency, and strategy-proofness, then for any problem for which the IR-core is non-empty, the allocation rule must choose an IR-core allocation and all agents are indifferent between all allocations in the IR-core. We further show that the result cannot be generalized to supersets of the IR-core. We apply our result to housing markets, coalition formation and networks.