Monotonicity and Envyfree Assignments
Given any problem involving assignment of indivisible objects and a sum of money among individuals, there is an efficient envy-free 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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Volume (Year): 4 (1994)
Issue (Month): 4 (May)
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