Econometrica: Jul, 1991, Volume 59, Issue 4

Fair Allocation of Indivisible Goods and Criteria of Justice

https://doi.org/0012-9682(199107)59:4<1023:FAOIGA>2.0.CO;2-5
p. 1023-1039

Ahmet Alkan, David Gale, Gabrielle Demange

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.