Abstract
This paper presents a constructive solution to the classic problem of land division. It is the first solution that enables the allocation of higher-dimensional resources without degenerating them first into a series of one-dimensional resource allocation problems. We base our allocation procedure on the topology of overlaps among the regions of interest of different agents. Our result is an algorithm suitable for computer implementation, unlike earlier ones that were only existential in nature. It uses the notion of degree of partial overlap to create a sufficiency condition for the existence of a solution, and proposes a procedure to find the overlaps in such a case. The proposed solution is fair, strategy-proof, non-existential, and does not explicitly need the resource to be measurable. The agents do not have to reveal their private utility functions. We extend our earlier result for one-dimensional resource allocation to this two-dimensional one and explain the distinctive issues involved.
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