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Fair Division of a Graph
Ayumi Igarashi (University of Oxford)
We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent’s share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents—or, less restrictively, the number of agent types—is small. In particular, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.
This is a joint work with Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, and Dominik Peters.
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