On the Fair and Efficient Allocation of Indivisible Commodities.
CORNELL UNIV ITHACA N Y SCHOOL OF OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING
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Auctions and fair division problems are situations in which commodities are to be allocated fairly and efficiently. While a variety of schemes exist for fairly allocating finely divisible homogeneous commodities, most schemes are not applicable to the problem of allocating indivisible items. This paper considers the problem of fairly allocation sets of indivisible objects. Dollars, a finely divisible, homogeneous, transferrable commodity, are used to evaluate individuals preferences and to transfer value among individuals. This introduction of dollars has several implications the main result is that fair allocation problems may be viewed as two smaller problems. First auction the goods among the individuals and then divide the resulting revenue according to the chosen definition of fairness. Several existing fair allocation schemes are reviewed examples illustrate some difficulties associated with their use. Kuhns definitions of fairness are presented and two extensions are considered for the case where individuals have different shares in the collection of goods.
- Operations Research