Abstract
In this work, we study the fair resource sharing problem, where a set of resources needs to be shared by a set of agents. Each agent is unit-demand and each resource can serve a limited number of agents. The agents have (heterogeneous) preferences for the resources, and preferences for other agents with whom they share the resources. Our definition of fairness is mainly captured by envy-freeness. Due to the fact that an envy-free assignment may not exist even in simple settings, we propose a way to relax the definition: Pareto envy-freeness, where an assignment is Pareto envy-free if for any two agents i and j, agent i does not envy agent j for her received resource or the set of agents she shares the resource with. We study to what extent Pareto envy-free assignments exist. Particularly, we are interested in a typical model, dorm assignment problem, where a number of students need to be accommodated to the dorms with the same capacity and the students’ preferences for dorm-mates are binary. We show that when the capacities of the dorms are 2, a Pareto envy-free assignment always exists and can be found in polynomial time; however, if the capacities increase to 3, Pareto envy-freeness cannot be guaranteed any more.
Published Version
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