Mixed fair division: A survey

S Liu, X Lu, M Suzuki, T Walsh - … of the AAAI Conference on Artificial …, 2024 - ojs.aaai.org
The fair allocation of resources to agents is a fundamental problem in society and has
received significant attention and rapid developments from the game theory and artificial …

Fair allocation with binary valuations for mixed divisible and indivisible goods

Y Kawase, K Nishimura, H Sumita - arxiv preprint arxiv:2306.05986, 2023 - arxiv.org
The fair allocation of mixed goods, consisting of both divisible and indivisible goods, has
been a prominent topic of study in economics and computer science. We define an …

A complete landscape for the price of envy-freeness

Z Li, S Liu, X Lu, B Tao, Y Tao - arxiv preprint arxiv:2401.01516, 2024 - arxiv.org
We study the efficiency of fair allocations using the well-studied price of fairness concept,
which quantitatively measures the worst-case efficiency loss when imposing fairness …

One Quarter Each (on Average) Ensures Proportionality

X Wu, C Zhang, S Zhou - International Conference on Web and Internet …, 2023 - Springer
We consider the problem of fair allocation of m indivisible items to a group of n agents with
subsidy (money). Our work mainly focuses on the allocation of chores but most of our results …

Fair division with subjective divisibility

X Bei, S Liu, X Lu - arxiv preprint arxiv:2310.00976, 2023 - arxiv.org
The classic fair division problems assume the resources to be allocated are either divisible
or indivisible, or contain a mixture of both, but the agents always have a predetermined and …

Minimizing symmetric convex functions over hybrid of continuous and discrete convex sets

Y Kawase, K Nishimura, H Sumita - 51st International Colloquium …, 2024 - drops.dagstuhl.de
We study the problem of minimizing a given symmetric strictly convex function over the
Minkowski sum of an integral base-polyhedron and an M-convex set. This problem has a …

Incentive Ratios for Fairly Allocating Indivisible Goods: Simple Mechanisms Prevail

B Tao, M Yang - arxiv preprint arxiv:2306.15920, 2023 - arxiv.org
We study the problem of fairly allocating indivisible goods among strategic agents.
Amanatidis et al. show that truthfulness is incompatible with any meaningful fairness notions …

Best-of-both-worlds fair allocation of indivisible and mixed goods

X Bu, Z Li, S Liu, X Lu, B Tao - arxiv preprint arxiv:2410.06877, 2024 - arxiv.org
We study the problem of fairly allocating either a set of indivisible goods or a set of mixed
divisible and indivisible goods (ie, mixed goods) to agents with additive utilities, taking the …

Tree Splitting Based Rounding Scheme for Weighted Proportional Allocations with Subsidy

X Wu, S Zhou - arxiv preprint arxiv:2404.07707, 2024 - arxiv.org
We consider the problem of allocating $ m $ indivisible items to a set of $ n $ heterogeneous
agents, aiming at computing a proportional allocation by introducing subsidy (money). It has …

Allocating Mixed Goods with Customized Fairness and Indivisibility Ratio

B Li, Z Li, S Liu, Z Wu - arxiv preprint arxiv:2404.18132, 2024 - arxiv.org
We consider the problem of fairly allocating a combination of divisible and indivisible goods.
While fairness criteria like envy-freeness (EF) and proportionality (PROP) can always be …