arXiv subjects

Fangxiao Wang

Publications and source records attributed to Fangxiao Wang.

6 recordsLinked to original sources

arXiv2026

How Well Can Strategyproof Tournament Rules Resist Pairwise Manipulation?

A tournament rule maps the outcomes of all pairwise matches among $n$ teams to a possibly randomized winner. Desirable rules should be Condorcet consistent and monotone, yet also resistant to manipulation among coalition. Prior work mostly measures such manipulation additively through $k$-strongly non-manipulable at $α$ ($k$-SNM-$α$), meaning that no coalition of size $k$ can fix the matches among themselves to increase their total winning probability by $α$. Very recently, two new notions of non-manipulability were introduced. Multiplicative non-manipulability ($k$-MNM-$δ$) is defined analogously, using the multiplicative factor instead. Non-manipulability for $λ$ ($k$-NM$_λ$) characterizes the selfishness of a team, which restricts a coalition's gain to be less than $λ$ times the winning probability sacrificed by its members. In this work, we begin with a strict hierarchy among these three notions: NM$_λ$ is stronger than MNM, which is then stronger than SNM. This motivates us to consider those two notions that are stronger but less studied: pairwise multiplicative non-manipulability and $2$-non-manipulability for $λ$. We show that Randomized Death Match is $2$-MNM-$3/2$ and optimally matches the lower bound. Then, we introduce the BlockBonusedWinStrengths rule, which is Condorcet consistent, monotone, and $2$-NM$_2$. This rule substantially improves the previous upper bound of $λ=11$ and comes within a factor of two of the lower bound $λ=1$.

cs.GT↗

arXiv2026

Constant Weighted Maximin Share Approximations for Chores

We study the fair allocation of indivisible chores among agents with asymmetric weights. Among the various fairness notions, weighted maximin share (WMMS) stands out as particularly compelling. Despite its appeal, the existence of a constant-factor approximation for WMMS has remained an important open problem in weighted fair division [Aziz et al., 2022, Suksompong, 2025]. Prior to our work, the best known approximation ratio was $O(\log n)$, where $n$ is the number of agents. In this paper, we make significant progress by presenting the first constant-factor approximation algorithm for WMMS. Our main contributions are as follows: [1] We design the first algorithm that guarantees a 12-approximate WMMS allocation, substantially improving upon the previous $O(\log n)$ upper bound. Our approach introduces a novel analytical framework based on canonical instance reductions, agent delegation, and proxy cost functions to effectively bound agents' costs. Additionally, we provide a polynomial-time implementation for any approximate WMMS algorithm, incurring a factor of 2 loss in the approximation ratio. [2] We present an improved worst-case lower bound, showing that no algorithm can achieve better than 2-approximate WMMS, thereby strengthening the previous best lower bound of 1.366. We further construct a general hard instance, which provides lower bounds for an arbitrary number of agents. [3] Beyond worst-case bounds, we precisely characterize the optimal approximation ratio curve for every possible weight distribution in the two-agent case. Notably, our results imply that a WMMS allocation may not exist for any two agents with different weights, in sharp contrast to the symmetric case where an MMS allocation always exists.

cs.GT↗

arXiv2026

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier

Maximin share (MMS) stands out as a central notion in fair resource allocation. It is known that exact MMS fairness is not always attainable, especially when agents differ along two dimensions: their valuations and their perceptions of the divisibility of resources. The former case with heterogeneous valuations has been widely studied in the literature. The latter, referred to as subjective divisibility by Bei et al., [Games Econ. Behav. 2025], remains much less explored. We study MMS approximation under subjective divisibility. First, we prove that even in the unary valuation setting, where all items have equal value, the optimal approximation ratio is 2/3. This result is somewhat surprising since in the objective setting, even when agents have heterogeneous valuations, the best possible approximation ratio is at least 7/9 [Huang and Zhou, 2025]. We then address the general case with both valuation heterogeneity and subjective divisibility. Previous work shows the existence of a 1/2-approximate MMS allocation. In this paper, we develop new algorithmic techniques that overcome the difficulties posed by subjective divisibility, and improve the approximation guarantee to 5/9. Finally, we complement this result with small-agent cases. For up to four agents, we give polynomial-time algorithms that compute 2/3-approximate MMS fair allocations. These bounds are tight. Our results deepen the understanding of MMS fairness under heterogeneous valuations and subjective divisibility, and provide a new perspective for this emerging model.

cs.GT↗

arXiv2026

Approximate Envy-Free Allocations up to any $k$ Goods

We study the problem of finding approximate envy-free allocations up to any $k$ goods ($α$-EFkX), when agents have additive values over goods in a bundle. As our main result, we show that for any $k>2$, $\frac{k+1}{k+2}$-EFkX allocations exist for any number of agents, and can be computed in polynomial time, via an appropriate generalization of the 3PA algorithm of [Amanatidis et al., 2024]. An immediate corollary of this result is that $3/4$-EF2X allocations exist for any number of agents; in contrast, $2/3$-EFX allocations are only known to exist for up to 7 agents. We improve this latter result by devising an algorithm that achieves $2/3$-EFX for 8 agents. We also consider EFkX graph orientations; we prove that such orientations do not always exist, and that deciding their existence is NP-complete, thereby generalizing the corresponding result of [Christodoulou et., 2023] for $k=1$.

cs.GT↗

arXiv2025

When is Truthfully Allocating Chores no Harder than Goods?

We study the problem of fairly and efficiently allocating a set of items among strategic agents with additive valuations, where items are either all indivisible or all divisible. When items are goods, numerous positive and negative results are known regarding the fairness and efficiency guarantees achievable by truthful mechanisms, whereas our understanding of truthful mechanisms for chores remains considerably more limited. In this paper, we discover various connections between truthful good and chore allocations, greatly enhancing our understanding of the latter via tools from the former. For indivisible chores with two agents, by leveraging the observation that a simple bundle-swapping operation transforms several properties for goods including truthfulness to the corresponding properties for chores, we characterize truthful mechanisms and derive tight guarantees of various fairness notions achieved by truthful mechanisms. Moreover, for homogeneous divisible chores, by generalizing the above transformation to an arbitrary number of agents, we characterize truthful mechanisms with two agents, show that every truthful mechanism with two agents admits an efficiency ratio of $0$, and derive a large family of strictly truthful, envy-free (EF), and proportional mechanisms for an arbitrary number of agents. Finally, for indivisible chores with an arbitrary number of agents having bi-valued cost functions, we give an ex-ante truthful, ex-ante Pareto optimal, ex-ante EF, and ex-post envy-free up to one item mechanism, improving the best guarantees for bi-valued instances by prior works.

cs.GT↗

arXiv2023

Fair Allocation of Indivisible Chores: Beyond Additive Costs

We study the maximin share (MMS) fair allocation of $m$ indivisible chores to $n$ agents who have costs for completing the assigned chores. It is known that exact MMS fairness cannot be guaranteed, and so far the best-known approximation for additive cost functions is $\frac{13}{11}$ by Huang and Segal-Halevi [EC, 2023]; however, beyond additivity, very little is known. In this work, we first prove that no algorithm can ensure better than $\min\{n,\frac{\log m}{\log \log m}\}$-approximation if the cost functions are submodular. This result also shows a sharp contrast with the allocation of goods where constant approximations exist as shown by Barman and Krishnamurthy [TEAC, 2020] and Ghodsi et al. [AIJ, 2022]. We then prove that for subadditive costs, there always exists an allocation that is $\min\{n,\lceil\log m\rceil\}$-approximation, and thus the approximation ratio is asymptotically tight. Besides multiplicative approximation, we also consider the ordinal relaxation, 1-out-of-$d$ MMS, which was recently proposed by Hosseini et al. [JAIR and AAMAS, 2022]. Our impossibility result implies that for any $d\ge 2$, a 1-out-of-$d$ MMS allocation may not exist. Due to these hardness results for general subadditive costs, we turn to studying two specific subadditive costs, namely, bin packing and job scheduling. For both settings, we show that constant approximate allocations exist for both multiplicative and ordinal relaxations of MMS.

cs.GT↗