Summary
Given any problem involving assignment of indivisible objects and a sum of money among individuals, there is an efficient envyfree allocation (namely the minmax money allocation) which can be extended monotonically to a new efficient envyfree allocation for any object added or individual removed, and another (the maximin value allocation) extendable similarly for any object removed or person added. Still, the efficient envyfree solution is largely incompatible with the resource and population monotonicity axioms: The minmax money and maxmin value allocations are unique in being extendable.
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I wish to thank William Thomson, David Gale, Ehud Kalai and a referee for valuable suggestions. Previous versions have appeared in the discussion paper series of CORE, Universite Catholique de Louvain, and CEME, Universite Libre de Brussels; to both of these centers I extend my thanks for the visit I enjoyed in 1992. I also gratefully acknowledge support from the Bogaziçi University Research Fund.
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Alkan, A. Monotonicity and envyfree assignments. Econ Theory 4, 605–616 (1994). https://doi.org/10.1007/BF01213627
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DOI: https://doi.org/10.1007/BF01213627