2025/03/03 by Kulkarni, Pooja, Mehta, Ruta, Shahkar, Parnian · 4 citations
#Computer Science and Game Theory (cs.GT) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Multiagent Systems (cs.MA)
paper · doi:10.48550/arxiv.2503.02088
We investigate the problem of fairly allocating m indivisible items among n 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 k-type fair division), a model that balances theoretical tractability with real-world applicability. In this model, each arriving agent belongs to one of k types, with all agents of a given type sharing the same known valuation function. We do not constrain k 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 (1)/(k)-MMS competitive algorithm and complement it with a lower bound, ruling out any Ω((1)/(√(k)))-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 k is unavoidable, we surprisingly show that in the stochastic setting, an asymptotic, arbitrarily close-to-(1)/(2)-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.