Complements and Substitutes in the Optimal Assignment Problem

by Lloyd S. Shapley


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When studying a process that depends intricately on several input activities, it is sometimes of interest to know whether two given activities are complements or substitutes — that is, whether they reinforce or interfere with each other's influence on the process as a whole.

In this research memorandum the "optimal assignment problem" is considered as such a process and the complementarity-substitutability relationships between its elements are rigorously established. Namely, it is shown that, in a standard interpretation of the problem, man-machine pairs are complementary while man-man and machine-machine pairs are substitutes.

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