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1. Robust Resource Allocation via Competitive Subsidies

   https://doi.org/10.4230/lipics.itcs.2026.96  

   Lin, David X; Fikioris, Giannis; Banerjee, Siddhartha; Tardos, Éva (January 2026, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Saraf, Shubhangi (Ed.)

   Abstract: A canonical setting for non-monetary online resource allocation is one where agents compete over multiple rounds for a single item per round, with i.i.d. valuations and additive utilities across rounds. With n symmetric agents, a natural benchmark for each agent is the utility realized by her favorite 1/n-fraction of rounds; a line of work has demonstrated one can robustly guarantee each agent a constant fraction of this ideal utility, irrespective of how other agents behave. In particular, several mechanisms have been shown to be 1/2-robust, and recent work established that repeated first-price auctions based on artificial credits have a robustness factor of 0.59, which cannot be improved beyond 0.6 using first-price and simple strategies. In contrast, even without strategic considerations, the best achievable factor is 1-1/e≈ 0.63. In this work, we break the 0.6 first-price barrier to get a new 0.625-robust mechanism, which almost closes the gap to the non-strategic robustness bound. Surprisingly, we do so via a simple auction, where in each round, bidders decide if they ask for the item, and we allocate uniformly at random among those who ask. The main new ingredient is the idea of competitive subsidies, wherein we charge the winning agent an amount in artificial credits that decreases when fewer agents are bidding (specifically, when k agents bid, then the winner pays proportional to k/(k+1), varying the payment by a factor of 2 depending on the competition). Moreover, we show how it can be modified to get an equilibrium strategy with a slightly weaker robust guarantee of 5/(3e) ≈ 0.61 (and the optimal 1-1/e factor at equilibrium). Finally, we show that our mechanism gives the best possible bound under a wide class of auction-based mechanisms. 

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2. Online Fair Allocation of Reusable Resources

   https://doi.org/10.1145/3727121  

   Liu, Qingsong; Hajiesmaili, Mohammad (May 2025, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   Motivated by the emerging paradigm of resource allocation that integrates classical objectives, such as cost minimization, with societal objectives, such as carbon awareness, this paper proposes a general framework for the online fair allocation of reusable resources. Within this framework, an online decision-maker seeks to allocate a finite resource with capacityCto a sequence of requests arriving with unknown distributions of types, utilities, and resource usage durations. To accommodate diverse objectives, the framework supports multiple actions and utility types, and the goal is to achieve max-min fairness among utilities, i.e., maximize the minimum time-averaged utility across all utility types. Our performance metric is an (α,β)-competitive guarantee of the form: ALG ≥ α • OPT^*- O(T^β-1),; α, β ∈ (0, 1], where OPT^*and ALG are the time-averaged optimum and objective value achieved by the decision maker, respectively. We propose a novel algorithm that achieves a competitive guarantee of (1-O(√(log C/C)), 2/3) under the bandit feedback. As resource capacity increases, the multiplicative competitive ratio term 1-O(√ logC/C) asymptotically approaches optimality. Notably, when the resource capacity exceeds a certain threshold, our algorithm achieves an improved competitive guarantee of (1, 2/3). Our algorithm employs an optimistic penalty-weight mechanism coupled with a dual exploration-discarding strategy to balance resource feasibility, exploration, and fairness among utilities. 

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3. Fair Allocation of Indivisible Goods: Improvement

   https://doi.org/10.1287/moor.2020.1096  

   Ghodsi, Mohammad; Hajiaghayi, Mohammad Taghi; Seddighin, Masoud; Seddighin, Saeed; Yami, Hadi (August 2021, Mathematics of Operations Research)

   null (Ed.)

   We study the problem of fair allocation for indivisible goods. We use the maximin share paradigm introduced by Budish [Budish E (2011) The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. J. Political Econom. 119(6):1061–1103.] as a measure of fairness. Kurokawa et al. [Kurokawa D, Procaccia AD, Wang J (2018) Fair enough: Guaranteeing approximate maximin shares. J. ACM 65(2):8.] were the first to investigate this fundamental problem in the additive setting. They showed that in delicately constructed examples, not everyone can obtain a utility of at least her maximin value. They mitigated this impossibility result with a beautiful observation: no matter how the utility functions are made, we always can allocate the items to the agents to guarantee each agent’s utility is at least 2/3 of her maximin value. They left open whether this bound can be improved. Our main contribution answers this question in the affirmative. We improve their approximation result to a 3/4 factor guarantee. 

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4. Ordinal Maximin Share Approximation for Goods

   https://doi.org/10.1613/jair.1.13317  

   Hosseini, Hadi; Searns, Andrew; Segal-Halevi, Erel (May 2022, Journal of Artificial Intelligence Research)

   In fair division of indivisible goods,  ℓ-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the ℓ least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' ordinal rankings of bundles. We prove the existence of ℓ-out-of-⌊(ℓ + 1/2)n⌋ MMS allocations of goods for any integer ℓ ≥ 1, and present a polynomial-time algorithm that finds a 1-out-of-⌈3n/2⌉ MMS allocation when ℓ=1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any ℓ > 1. 

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5. Approximating Maximin Share Allocations

   https://doi.org/10.4230/OASIcs.SOSA.2019.20  

   Garg, Jugal; McGlaughlin, Peter; Taki, Setareh (January 2019, Open access series in informatics)

   We study the problem of fair allocation of M indivisible items among N agents using the popular notion of maximin share as our measure of fairness. The maximin share of an agent is the largest value she can guarantee herself if she is allowed to choose a partition of the items into N bundles (one for each agent), on the condition that she receives her least preferred bundle. A maximin share allocation provides each agent a bundle worth at least their maximin share. While it is known that such an allocation need not exist [Procaccia and Wang, 2014; Kurokawa et al., 2016], a series of work [Procaccia and Wang, 2014; David Kurokawa et al., 2018; Amanatidis et al., 2017; Barman and Krishna Murthy, 2017] provided 2/3 approximation algorithms in which each agent receives a bundle worth at least 2/3 times their maximin share. Recently, [Ghodsi et al., 2018] improved the approximation guarantee to 3/4. Prior works utilize intricate algorithms, with an exception of [Barman and Krishna Murthy, 2017] which is a simple greedy solution but relies on sophisticated analysis techniques. In this paper, we propose an alternative 2/3 maximin share approximation which offers both a simple algorithm and straightforward analysis. In contrast to other algorithms, our approach allows for a simple and intuitive understanding of why it works. 

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