
When Do EnvyFree Allocations Exist?
We consider a fair division setting in which m indivisible items are to ...
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On the Number of Almost EnvyFree Allocations
Envyfreeness is a standard benchmark of fairness in resource allocation...
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FairnessEfficiency Tradeoffs in Dynamic Fair Division
We investigate the tradeoffs between fairness and efficiency when alloca...
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Contiguous Cake Cutting: Hardness Results and Approximation Algorithms
We study the fair allocation of a cake, which serves as a metaphor for a...
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Fair allocation of combinations of indivisible goods and chores
We consider the problem of fairly dividing a set of items. Much of the f...
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Picking Sequences and Monotonicity in Weighted Fair Division
We study the problem of fairly allocating indivisible items to agents wi...
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On Interim EnvyFree Allocation Lotteries
With very few exceptions, recent research in fair division has mostly fo...
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Closing Gaps in Asymptotic Fair Division
We study a resource allocation setting where m discrete items are to be divided among n agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common fairness notions like envyfreeness and proportionality cannot always be satisfied in this setting, an important question is when allocations satisfying these notions exist. In this paper, we close several gaps in the line of work on asymptotic fair division. First, we prove that the classical roundrobin algorithm is likely to produce an envyfree allocation provided that m=Ω(nlog n/loglog n), matching the lower bound from prior work. We then show that a proportional allocation exists with high probability as long as m≥ n, while an allocation satisfying envyfreeness up to any item (EFX) is likely to be present for any relation between m and n. Finally, we consider a related setting where each agent is assigned exactly one item and the remaining items are left unassigned, and show that the transition from nonexistence to existence with respect to envyfree assignments occurs at m=en.
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