New Round-Robin Protocol Ensures Fair Allocation for Multiple AI Agents

A new paper from Georgios Amanatidis and co-authors tackles the challenge of fair resource allocation when multiple AI agents each need to maximize their own submodular objective—a function modeling diminishing returns—over a shared set of items, subject to individual constraints like capacity limits (p-systems). The key innovation is a simple Round-Robin protocol where agents take turns picking items, each using their own internal algorithm. The protocol itself performs no computation, making it highly scalable and decentralized.

The analysis shows that greedy agents (those picking the highest marginal gain at each turn) enjoy strong theoretical guarantees. For monotone objectives, a greedy agent with a p_i-system constraint achieves a 1/(n+p_i) fraction of their optimal value when they first choose. In competition-robust scenarios, this improves to a 1/Θ(p_i) approximation of the unconstrained optimum—asymptotically optimal in polynomial time. The paper also establishes novel fairness properties: the resulting allocations are approximately feasible-envy-free-up-to-one-item (FEF1) and feasible-envy-free-towards-unallocated-items (FEFu). Furthermore, via an augmented protocol and a polynomial-time proxy, they provide the first Θ(1/p_i)-approximate feasible maximin share (FMMS) guarantees for submodular agents with combinatorial constraints. Finally, they prove that consistently outperforming greedy policies is NP-hard even in simple settings.