In the field of multiagent systems, one important problem is fairly allocating items among a set of agents. The gold standard fairness property is envy-freeness whereby each agent prefers the bundle allocated to them over any other bundle. For indivisible goods, envy-freeness cannot be guaranteed: consider two agents and one item. In the context of indivisible goods, one key fairness notion which has gained significant attention in recent years is the maximin share guarantee (MMS). MMS extends the cut-and-choose protocol to multiple agents by guaranteeing each agent as much value as if they divided items into bundles but chose last. However, MMS is not guaranteed to exist, and even it exists, computing an MMS allocation is computationally hard. Consequently, several approximation techniques were proposed to ensure all agents receive a fraction of their MMS.

We propose an orthogonal approximation which aims to guarantee MMS for a fraction of the agents. We construct instances where any optimal approximation algorithm fails to guarantee MMS for most agents. We show how to interpolate between the fraction of agents and the fraction of MMS guaranteed to agents. We prove the existence of allocations which satisfy 2/3 of the agents. Our algorithmic technique immediately implies a polynomial-time algorithm for any number of items when there are less than nine agents. Our results significantly reduce the existence gap of MMS when agents divide the items into 3n/2 bundles. We empirically demonstrate that our algorithm outperforms its worst-case bounds in practice on both synthetic and real-world data.

We extend our discussion of maximin share approximations to chores. We extend many of the techniques used for MMS approximations to the chores setting. Using these new techniques, we prove the existence of allocations which satisfy all agents when they expect to divide the workload among 2n/3 agents.

Library of Congress Subject Headings

Resource allocation--Mathematical models; Multiagent systems--Mathematical models; Approximation algorithms

Publication Date


Document Type


Student Type


Degree Name

Computer Science (MS)

Department, Program, or Center

Computer Science (GCCIS)


Hadi Hosseini

Advisor/Committee Member

Ivona Bezakova

Advisor/Committee Member

Stanislaw Radziszowski


RIT – Main Campus

Plan Codes