
Fair Division with Bounded Sharing
A set of objects is to be divided fairly among agents with different tas...
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Fair Division with Minimal Sharing
A set of objects, some goods and some bads, is to be divided fairly amon...
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ConsenusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
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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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ConsensusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
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Fair Cake Division Under Monotone Likelihood Ratios
This work develops algorithmic results for the classic cakecutting prob...
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Disproportionate division
We study the disproportionate version of the classical cakecutting prob...
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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 divide a set of chores (bads) among themselves fairly and efficiently. We assume that agents have linear disutility (cost) functions. Like for the case of goods, competitive division is known to be arguably the best mechanism for the bads as well. However, unlike goods, there are multiple competitive divisions with very different disutility value profiles in bads. Although all competitive divisions satisfy the standard notions of fairness and efficiency, some divisions are significantly fairer and efficient than the others. This raises two important natural questions: Does there exist a competitive division in which no agent is assigned a chore that she hugely dislikes? Are there simple sufficient conditions for the existence and polynomialtime algorithms assuming them? We investigate both these questions in this paper. We show that the first problem is strongly NPhard. Further, we derive a simple sufficient condition for the existence, and we show that finding a competitive division is PPADhard assuming the condition. These results are in sharp contrast to the case of goods where both problems are strongly polynomialtime solvable. To the best of our knowledge, these are the first hardness results for the chore division problem, and, in fact, for any economic model under linear preferences.
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