Maximin Share Guarantees via Limited Cost-Sensitive Sharing

Researchers Hana Salavcova, Martin Černý, and Arpita Biswas published a paper titled 'Maximin Share Guarantees via Limited Cost-Sensitive Sharing' on arXiv on February 24, 2026, addressing the challenge of fairly allocating indivisible goods when limited sharing is permitted among multiple agents. The paper explores scenarios where each good can be allocated to up to k agents while incurring a sharing cost, demonstrating that controlled sharing can restore fairness guarantees that are otherwise unattainable in certain resource allocation problems. This research was prepared for presentation at the 25th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2026) in Paphos, Cyprus, scheduled for May 25-29, 2026. The core problem addressed is that classic maximin share (MMS) allocations often do not exist in many real-world scenarios involving indivisible goods. The researchers introduce the concept of cost-sensitive sharing, where goods can be shared among multiple agents but at a computational cost. Their theoretical framework bridges game theory and artificial intelligence, offering new algorithms and fairness concepts for multi-agent environments where resources cannot be perfectly divided. The study provides both theoretical guarantees and practical algorithms that can be implemented in various resource allocation systems. The paper makes six significant contributions: first, it proves that exact MMS allocations exist when goods can be shared among at least half of agents with even numbers; second, it introduces a Shared Bag-Filling Algorithm that guarantees a (1 - C)(k - 1)-approximate MMS allocation; third, it proposes the Sharing Maximin Share (SMMS) fairness notion; fourth, it demonstrates SMMS allocations always exist with identical utilities and two-agent scenarios; fifth, it presents a counterexample showing SMMS allocations don't universally exist; and sixth, it establishes connections between SMMS and constrained MMS for approximation guarantees. This research has significant implications for various fields including economics, artificial intelligence, and distributed systems, where fair resource allocation is critical. The findings enable more practical implementation of fair division principles in real-world scenarios where perfect division of resources is impossible, potentially improving outcomes in everything from cloud computing resource allocation to fair division of physical assets among multiple stakeholders.