Fairly Allocating (Contiguous) Dynamic Indivisible Items with Few Adjustments

by   Mingwei Yang, et al.

We study the problem of dynamically allocating indivisible items to a group of agents in a fair manner. Due to the negative results to achieve fairness when allocations are irrevocable, we allow adjustments to make fairness attainable with the objective to minimize the number of adjustments. For restricted additive or general identical valuations, we show that envy-freeness up to one item (EF1) can be achieved at no cost. For additive valuations, we give an EF1 algorithm that requires O(mT) adjustments, where m is the maximum number of different valuations for items among all agents. We further impose the contiguity constraint on items and require that each agent obtains a consecutive block of items. We present extensive results to achieve either proportionality with an additive approximate factor or EF1. In particular, we establish matching lower and upper bounds for identical valuations to achieve approximate proportionality. We also show that it's hopeless to make any significant improvement when valuations are nonidentical. Our results exhibit a large discrepancy between the identical and nonidentical cases in both contiguous and noncontiguous settings. All our positive results are computationally efficient.


page 1

page 2

page 3

page 4


Fair allocation of a multiset of indivisible items

We study the problem of allocating a set M of m indivisible items among ...

Repeatedly Matching Items to Agents Fairly and Efficiently

We consider a novel setting where a set of items are matched to the same...

On the Price of Fairness of Allocating Contiguous Blocks

In this work, we revisit the problem of fairly allocating a number of in...

On allocations that give intersecting groups their fair share

We consider item allocation to individual agents who have additive valua...

On Fair Division under Heterogeneous Matroid Constraints

We study fair allocation of indivisible goods among additive agents with...

Fairness-Efficiency Tradeoffs in Dynamic Fair Division

We investigate the tradeoffs between fairness and efficiency when alloca...

On the Existence of Envy-Free Allocations Beyond Additive Valuations

We study the problem of fairly allocating m indivisible items among n ag...

Please sign up or login with your details

Forgot password? Click here to reset