Maximin Share Guarantees via Limited Cost-Sensitive Sharing

Computer scientists Hana Salavcova, Martin Černý, and Arpita Biswill present groundbreaking theoretical work on fair resource allocation in multi-agent AI systems at the 25th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2026). Their paper 'Maximin Share Guarantees via Limited Cost-Sensitive Sharing' addresses a fundamental problem in AI and game theory: how to fairly divide indivisible resources among multiple agents when classic fairness guarantees (maximin share or MMS allocations) often don't exist. The researchers demonstrate that allowing controlled sharing—where each item can be allocated to up to k agents with associated sharing costs—can restore fairness guarantees that are otherwise impossible in many scenarios.

Their key technical contributions include proving that exact MMS allocations are guaranteed to exist when goods can be shared among at least half of the agents, with even numbers of agents achieving full MMS guarantees. They also introduce the Shared Bag-Filling Algorithm that provides (1-C)(k-1)-approximate MMS allocations, where C represents the maximum cost of sharing a good and k is the sharing limit. When (1-C)(k-1) ≥ 1, the algorithm recovers exact MMS allocations. The team further develops the Sharing Maximin Share (SMMS) fairness notion as a natural extension of MMS to k-sharing settings, establishing connections to constrained MMS (CMMS) and providing approximation guarantees. While they show SMMS allocations always exist under identical utilities and for two-agent instances, they also construct counterexamples demonstrating the impossibility of universal SMMS existence.