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Fair Allocation of Indivisible Goods and Criteria of Justice
Ahmet Alkan
Gabrielle Demange
David Gale
Abstract
A set of $n$ objects and an amount $M$ of money is to be distributed among $m$ people. Example: the objects are tasks and the money is compensation from a fixed budget. An elementary argument via constrained optimization shows that for $M$ sufficiently large the set of efficient, envy free allocations is nonempty and has a nice structure. In particular, various criteria of justice lead to unique best fair allocations which are well behaved with respect to changes of $M$. This is in sharp contrast to the usual fair division theory with divisible goods.
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