We investigate the problem of fairly allocating indivisible items among sequentially arriving agents with additive valuations, under the sought-after fairness notion of maximin share (MMS). We first observe a strong impossibility: without appropriate knowledge about the valuation functions of the incoming agents, no online algorithm can ensure any non-trivial MMS approximation, even when there are only two agents. Motivated by this impossibility, we introduce OnlineKTypeFD (online -type fair division), a model that balances theoretical tractability with real-world applicability. In this model, each arriving agent belongs to one of types, with all agents of a given type sharing the same known valuation function. We do not constrain to be a constant. Upon arrival, an agent reveals her type, receives an irrevocable allocation, and departs. We study the ex-post MMS guarantees of online algorithms under two arrival models:1- Adversarial arrivals: In this model, an adversary determines the type of each arriving agent. We design a -MMS competitive algorithm and complement it with a lower bound, ruling out any -MMS-competitive algorithm, even for binary valuations.2- Stochastic arrivals: In this model, the type of each arriving agent is independently drawn from an underlying, possibly unknown distribution. Unlike the adversarial setting where the dependence on is unavoidable, we surprisingly show that in the stochastic setting, an asymptotic, arbitrarily close-to--MMS competitive guarantee is achievable under mild distributional assumptions.Our results extend naturally to a learning-augmented framework; when given access to predictions about valuation functions, we show that the competitive ratios of our algorithms degrade gracefully with multiplicative prediction errors.
View on arXiv@article{kulkarni2025_2503.02088,
title={ Online Fair Division: Towards Ex-Post Constant MMS Guarantees },
author={ Pooja Kulkarni and Ruta Mehta and Parnian Shahkar },
journal={arXiv preprint arXiv:2503.02088},
year={ 2025 }
}