
Fair Division with Bounded Sharing
A set of objects is to be divided fairly among agents with different tas...
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Asymptotic Existence of Proportionally Fair Allocations
Fair division has long been an important problem in the economics litera...
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Fully PolynomialTime Approximation Schemes for Fair Rent Division
We study the problem of fair rent division that entails splitting the re...
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Dividing Bads is Harder than Dividing Goods: On the Complexity of Fair and Efficient Division of Chores
We study the chore division problem where a set of agents needs to divid...
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A simple Online Fair Division problem
A fixed set of n agents share a random object: the distribution μ of the...
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Fair Resource Sharing with Externailities
We study a fair resource sharing problem, where a set of resources are t...
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CakeCutting with Different Entitlements: How Many Cuts are Needed?
A cake has to be divided fairly among n agents. When all agents have equ...
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Fair Division with Minimal Sharing
A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utilityfunctions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. What is the smallest number of objects that must be shared between two or more agents in order to attain a fair division? We focus on Paretooptimal, envyfree and/or proportional allocations. We show that, for a generic instance of the problem — all instances except of a zeromeasure set of degenerate problems — a fair and Paretooptimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where the agents' valuations are aligned for many objects.
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