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Biaoshuai Tao

Publications and source records attributed to Biaoshuai Tao.

At least 37 records · Page 2Linked to original sources

arXiv2025

On Pareto-Optimal and Fair Allocations with Personalized Bi-Valued Utilities

We study the fair division problem of allocating $m$ indivisible goods to $n$ agents with additive personalized bi-valued utilities. Specifically, each agent $i$ assigns one of two positive values $a_i > b_i > 0$ to each good, indicating that agent $i$'s valuation of any good is either $a_i$ or $b_i$. For convenience, we denote the value ratio of agent $i$ as $r_i = a_i / b_i$. We give a characterization to all the Pareto-optimal allocations. Our characterization implies a polynomial-time algorithm to decide if a given allocation is Pareto-optimal in the case each $r_i$ is an integer. For the general case (where $r_i$ may be fractional), we show that this decision problem is coNP-complete. Our result complements the existing results: this decision problem is coNP-complete for tri-valued utilities (where each agent's value for each good belongs to $\{a,b,c\}$ for some prescribed $a>b>c\geq0$), and this decision problem belongs to P for bi-valued utilities (where $r_i$ in our model is the same for each agent). We further show that an EFX allocation always exists and can be computed in polynomial time under the personalized bi-valued utilities setting, which extends the previous result on bi-valued utilities. We propose the open problem of whether an EFX and Pareto-optimal allocation always exists (and can be computed in polynomial time).

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arXiv2025

Online MMS Allocation for Chores

We study the problem of fair division of indivisible chores among $n$ agents in an online setting, where items arrive sequentially and must be allocated irrevocably upon arrival. The goal is to produce an $α$-MMS allocation at the end. Several recent works have investigated this model, but have only succeeded in obtaining non-trivial algorithms under restrictive assumptions, such as the two-agent bi-valued special case (Wang and Wei, 2025), or by assuming knowledge of the total disutility of each agent (Zhou, Bai, and Wu, 2023). For the general case, the trivial $n$-MMS guarantee remains the best known, while the strongest lower bound is still only $2$. We close this gap on the negative side by proving that for any fixed $n$ and $\varepsilon$, no algorithm can guarantee an $(n - \varepsilon)$-MMS allocation. Notably, this lower bound holds precisely for every $n$, without hiding constants in big-$O$ notation, thereby exactly matching the trivial upper bound. Despite this strong impossibility result, we also present positive results. We provide an online algorithm that applies in the general case, guaranteeing a $\min\{n, O(k), O(\log D)\}$-MMS allocation, where $k$ is the maximum number of distinct disutilities across all agents and $D$ is the maximum ratio between the largest and smallest disutilities for any agent. This bound is reasonable across a broad range of scenarios and, for example, implies that we can achieve an $O(1)$-MMS allocation whenever $k$ is constant. Moreover, to optimize the constant in the important personalized bi-valued case, we show that if each agent has at most two distinct disutilities, our algorithm guarantees a $(2 + \sqrt{3}) \approx 3.7$-MMS allocation.

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arXiv2025

Incentive Analysis of Collusion in Fair Division

We study fair division problems with strategic agents capable of gaining advantages by manipulating their reported preferences. Although several impossibility results have revealed the incompatibility of truthfulness with standard fairness criteria, subsequent works have circumvented this limitation through the incentive ratio framework. Previous studies demonstrate that fundamental mechanisms like Maximum Nash Welfare (MNW) and Probabilistic Serial (PS) for divisible goods, and Round-Robin (RR) for indivisible goods achieve an incentive ratio of $2$, implying that no individual agent can gain more than double his truthful utility through manipulation. However, collusive manipulation by agent groups remains unexplored. In this work, we define strong group incentive ratio (SGIR) and group incentive ratio (GIR) to measure the gain of collusive manipulation, where SGIR and GIR are respectively the maximum and minimum of the incentive ratios of corrupted agents. Then, we tightly characterize the SGIRs and GIRs of MNW, PS, and RR. In particular, the GIR of MNW is $2$ regardless of the coalition size. Moreover, for coalition size $c \geq 1$, the SGIRs of MNW and PS, and the GIRs of PS and RR are $c + 1$. Finally, the SGIR of RR is unbounded for coalition size $c \geq 2$. Our results reveal fundamental differences of these three mechanisms in their vulnerability to collusion.

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arXiv2025

Logarithmic Comparison-Based Query Complexity for Fair Division of Indivisible Goods

We study the problem of fairly allocating $m$ indivisible goods to $n$ agents, where agents may have different preferences over the goods. In the traditional setting, agents' valuations are provided as inputs to the algorithm. In this paper, we adopt the query model, which has been widely considered for other similar problems (such as matching [Nis21], graph isomorphism [OS18], and equilibrium in game [Bab16]), and apply it to the fair division problem. In particular, we consider a new \emph{comparison-based query model}, where the algorithm presents two bundles of goods to an agent and the agent responds by telling the algorithm which bundle she prefers. We investigate the query complexity for computing allocations with several fairness notions, including \emph{proportionality up to one good} (PROP1), \emph{envy-freeness up to one good} (EF1), and \emph{maximin share} (MMS). Our main result is an algorithm that computes an allocation that satisfies both PROP1 and $\frac12$-MMS within $O(\log m)$ queries with a constant number of $n$ agents. For identical and additive valuation, we present an algorithm for computing an EF1 allocation within $O(\log m)$ queries with a constant number of $n$ agents. To complement the positive results, we show that the lower bound of the query complexity for any of the three fairness notions is $Ω(\log m)$ even with two agents.

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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.

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arXiv2025

Fair Division with Allocator's Preference

We study the fair allocation of indivisible resources among agents. Most prior work focuses on fairness and/or efficiency among agents. However, the allocator, as the resource owner, may also be involved in many scenarios (e.g., government resource allocation, heritage division, company personnel assignment, etc). The allocator inclines to obtain a fair or efficient allocation based on her preference over the items and to whom each item is allocated. We propose a model and study two problems: 1) Find an allocation fair to both agents and allocator; 2) Maximize allocator's efficiency under agents' fairness. We consider the two fundamental fairness criteria: envy-freeness and proportionality. For the first problem, we study the existence of an allocation that is envy-free up to $c$ goods (EF-$c$) or proportional up to $c$ goods (PROP-$c$) from both the agents' and the allocator's perspectives, called doubly EF-$c$ or doubly PROP-$c$. When the allocator's utility only depends on the items (not recipients), we prove that a doubly EF-$1$ allocation always exists. For the general setting where the allocator has a preference over the items and to whom each item is allocated, a doubly EF-$1$ allocation always exists for two agents, a doubly PROP-$2$ allocation always exists for personalized bi-valued valuations, and a doubly PROP-$O(\log n)$ allocation always exists. For the second problem, we give (in)approximability results with asymptotically tight bounds in most settings. When agents' valuations are binary, maximizing the allocator's social welfare while ensuring agents' fairness criteria of PROP-$c$ (with a general number of agents) and EF-$c$ (with a constant number of agents) are both polynomial-time solvable for any integer $c$. Strong inapproximability holds for most of the other settings (general valuations, EF-$c$, etc).

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arXiv2025

Approximability Landscape of Welfare Maximization within Fair Allocations

Fair allocation of indivisible goods studies allocating $m$ goods among $n$ agents in a fair manner. While fairness is a fundamental requirement in many real-world applications, it often conflicts with (economic) efficiency. This raises a natural and important question: How can we identify the most welfare-efficient allocation among all fair allocations? This paper answers from the perspective of computational complexity. Specifically, we study the problem of maximizing utilitarian social welfare under two widely studied fairness criteria: envy-freeness up to any item (EFX) and envy-freeness up to one item (EF1). We examine both normalized and unnormalized valuations, where normalized valuations require that each agent's total utility for all items is identical. The key contributions of this paper can be summarized as follows: (i) we sketch the complete complexity landscape of welfare maximization subject to fair allocation constraints; and (ii) we provide interesting bounds on the price of fairness for both EFX and EF1. Specifically: (1) For $n=2$ agents, we develop polynomial-time approximation schemes (PTAS) and provide NP-hardness results for EFX and EF1 constraints; (2) For $n>2$ agents, under EFX constraints, we design algorithms that achieve approximation ratios of $O(n)$ and $O(\sqrt{n})$ for unnormalized and normalized valuations, respectively. These results are complemented by asymptotically tight inapproximability results. We also obtain similar results for EF1 constraints; (3) When the number of agents is a fixed constant, we show that the optimal solution can be computed in polynomial time by slightly relaxing the fairness constraints, whereas exact fairness leads to strong inapproximability; (4) Furthermore, our results imply the price of EFX is $Θ(\sqrt{n})$ for normalized valuations, which is unknown in the literature.

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arXiv2025

The Art of Two-Round Voting

We study the voting problem with two alternatives where voters' preferences depend on a not-directly-observable state variable. While equilibria in the one-round voting mechanisms lead to a good decision, they are usually hard to compute and follow. We consider the two-round voting mechanism where the first round serves as a polling stage and the winning alternative only depends on the outcome of the second round. We show that the two-round voting mechanism is a powerful tool for making collective decisions. Firstly, every (approximated) equilibrium in the two-round voting mechanisms (asymptotically) leads to the decision preferred by the majority as if the state of the world were revealed to the voters. Moreover, there exist natural equilibria in the two-round game following intuitive behaviors such as informative voting, sincere voting [Austen-Smith and Banks, 1996], and the surprisingly popular strategy [Prelec et al., 2017]. This sharply contrasts with the one-round voting mechanisms in the previous literature, where no simple equilibrium is known. Finally, we show that every equilibrium in the standard one-round majority vote mechanism gives an equilibrium in the two-round mechanisms that is not more complicated than the one-round equilibrium. Therefore, the two-round voting mechanism provides a natural equilibrium in every instance, including those where one-round voting fails to have a natural solution, and it can reach an informed majority decision whenever one-round voting can. Our experiments on generative AI voters also imply that two-round voting leads to the correct outcome more often than one-round voting under some circumstances.

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arXiv2025

Aggregating Information and Preferences with Bounded-Size Deviations

We investigate a voting scenario with two groups of agents whose preferences depend on a ground truth that cannot be directly observed. The majority's preferences align with the ground truth, while the minorities disagree. Focusing on strategic behavior, we analyze situations where agents can form coalitions up to a certain capacity and adopt the concept of ex-ante Bayesian $k$-strong equilibrium, in which no group of at most $k$ agents has an incentive to deviate. Our analysis provides a complete characterization of the region where equilibria exist and yield the majority-preferred outcome when the ground truth is common knowledge. This region is defined by two key parameters: the size of the majority group and the maximum coalition capacity. When agents cannot coordinate beyond a certain threshold determined by these parameters, a stable outcome supporting the informed majority emerges. The boundary of this region exhibits several distinct segments, notably including a surprising non-linear relationship between majority size and deviation capacity. Our results reveal the complexity of the strategic behaviors in this type of voting game, which in turn demonstrate the capability of the ex-ante Bayesian $k$-strong equilibrium to provide a more detailed analysis.

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arXiv2025

The Incentive Guarantees Behind Nash Welfare in Divisible Resources Allocation

We study the problem of allocating divisible resources among $n$ agents, hopefully in a fair and efficient manner. With the presence of strategic agents, additional incentive guarantees are also necessary, and the problem of designing fair and efficient mechanisms becomes much less tractable. While there are flourishing positive results against strategic agents for homogeneous divisible items, very few of them are known to hold in cake cutting. We show that the Maximum Nash Welfare (MNW) mechanism, which provides desirable fairness and efficiency guarantees and achieves an incentive ratio of $2$ for homogeneous divisible items, also has an incentive ratio of $2$ in cake cutting. Remarkably, this result holds even without the free disposal assumption, which is hard to get rid of in the design of truthful cake cutting mechanisms. Moreover, we show that, for cake cutting, the Partial Allocation (PA) mechanism proposed by Cole et al. (EC'13), which is truthful and $1/e$-MNW for homogeneous divisible items, has an incentive ratio between $[e^{1 / e}, e]$ and when randomization is allowed, can be turned to be truthful in expectation. Given two alternatives for a trade-off between incentive ratio and Nash welfare provided by the MNW and PA mechanisms, we establish an interpolation between them for both cake cutting and homogeneous divisible items. Finally, we study the optimal incentive ratio achievable by envy-free cake cutting mechanisms. We first give an envy-free mechanism for two agents with an incentive ratio of $4 / 3$. Then, we show that any envy-free cake cutting mechanism with the connected pieces constraint has an incentive ratio of $Θ(n)$.

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arXiv2025

A Thorough Comparison Between Independent Cascade and Susceptible-Infected-Recovered Models

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an "out-going-edge-correlated" version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model. Finally, we conduct experimental studies over real-world datasets.

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arXiv2025

The Degree of (Extended) Justified Representation and Its Optimization

Justified Representation (JR)/Extended Justified Representation (EJR) is a desirable axiom in multiwinner approval voting. In contrast to that (E)JR only requires at least \emph{one} voter to be represented in every cohesive group, we study its optimization version that maximizes the \emph{number} of represented voters in each group. Given an instance, we say a winning committee provides a JR degree (EJR degree, resp.) of $c$ if at least $c$ voters in each $\ell$-cohesive group ($1$-cohesive group, resp.) have approved $\ell$ ($1$, resp.) winning candidates. Hence, every (E)JR committee provides the (E)JR degree of at least $1$. Besides proposing this new property, we propose the optimization problem of finding a winning committee that achieves the maximum possible (E)JR degree, called \MDJR and \MDEJR, corresponding to JR and EJR respectively. We study the computational complexity and approximability of \MDJR of \MDEJR. An (E)JR committee, which can be found in polynomial time, straightforwardly gives a $(k/n)$-approximation. We also show that the original algorithms for finding a JR and an EJR winner committee are also $1/k$ and $1/(k+1)$ approximation algorithms for \MDJR and \MDEJR respectively. On the other hand, we show that it is NP-hard to approximate \MDJR and \MDEJR to within a factor of $\left(k/n\right)^{1-ε}$ and to within a factor of $(1/k)^{1-\varepsilon}$, for any $ε>0$, which complements the positive results. Next, we study the fixed-parameter-tractability of this problem. We show that both problems are W[2]-hard if $k$, the size of the winning committee, is specified as the parameter. However, when $c_{\text{max}}$, the maximum value of $c$ such that a committee that provides an (E)JR degree of $c$ exists, is additionally given as a parameter, we show that both \MDJR and \MDEJR are fixed-parameter-tractable.

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arXiv2025

Strong Equilibria in Bayesian Games with Bounded Group Size

We study the group strategic behaviors in Bayesian games. Equilibria in previous work do not consider group strategic behaviors with bounded sizes and are too ``strong'' to exist in many scenarios. We propose the ex-ante Bayesian $k$-strong equilibrium and the Bayesian $k$-strong equilibrium, where no group of at most $k$ agents can benefit from deviation. The two solution concepts differ in how agents calculate their utilities when contemplating whether a deviation is beneficial. Intuitively, agents are more conservative in the Bayesian $k$-strong equilibrium than in the ex-ante Bayesian $k$-strong equilibrium. With our solution concepts, we study collusion in the peer prediction mechanisms, as a representative of the Bayesian games with group strategic behaviors. We characterize the thresholds of the group size $k$ so that truthful reporting in the peer prediction mechanism is an equilibrium for each solution concept, respectively. Our solution concepts can serve as criteria to evaluate the robustness of a peer prediction mechanism against collusion. Besides the peer prediction problem, we also discuss two other potential applications of our new solution concepts, voting and Blotto games, where introducing bounded group sizes provides more fine-grained insights into the behavior of strategic agents.

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arXiv2024

Best-of-Both-Worlds Fair Allocation of Indivisible and Mixed Goods

We study the problem of fairly allocating either a set of indivisible goods or a set of mixed divisible and indivisible goods (i.e., mixed goods) to agents with additive utilities, taking the best-of-both-worlds perspective of guaranteeing fairness properties both ex ante and ex post. The ex-post fairness notions considered in this paper are relaxations of envy-freeness, specifically, EFX for indivisible-goods allocation, and EFM for mixed-goods allocation. For two agents, we show that there is a polynomial-time randomized algorithm that achieves ex-ante envy-freeness and ex-post EFX / EFM simultaneously. For $n$ agents with bi-valued utilities, we show there exist randomized allocations that are (i) ex-ante proportional and ex-post EFM, and (ii) ex-ante envy-free, ex-post EFX, and ex-post fractionally Pareto optimal.

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arXiv2024

Aggregation of Antagonistic Contingent Preferences: When Is It Possible?

We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can collaborate in a group and have antagonistic preferences -- given the revealed world state, voters will support different alternatives. We identify sharp thresholds for the fraction of the majority-type voters necessary for preference aggregation. We specifically examine the majority vote mechanism (where each voter has one vote, and the alternative with more votes wins) and pinpoint a critical threshold, denoted as $θ_{\texttt{maj}}$, for the majority-type proportion. When the fraction of majority-type voters surpasses $θ_{\texttt{maj}}$, there is a symmetric strategy for the majority-type that leads to strategic equilibria favoring informed majority decisions. Conversely, when the majority-type proportion falls below $θ_{\texttt{maj}}$, equilibrium does not exist, rendering the aggregation of informed majority decisions impossible. Additionally, we propose an easy-to-implement mechanism that establishes a lower threshold $θ^\ast$ (with $θ^\ast \leq θ_{\texttt{maj}}$) for both equilibria and informed majority decision aggregation. We demonstrate that $θ^\ast$ is optimal by proving a general impossibility result: if the majority-type proportion is below $θ^\ast$, with mild assumptions, no mechanism can aggregate the preferences, meaning that no equilibrium leads to the informed majority decision for any mechanism.

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arXiv2024

Fair and Almost Truthful Mechanisms for Additive Valuations and Beyond

We study the problem of fairly allocating indivisible goods among $n$ strategic agents. It is well-known that truthfulness is incompatible with any meaningful fairness notions. We bypass the strong negative result by considering the concept of incentive ratio, a relaxation of truthfulness quantifying agents' incentive to misreport. Previous studies show that Round-Robin, which satisfies envy-freeness up to one good (EF1), achieves an incentive ratio of $2$ for additive valuations. In this paper, we explore the incentive ratio achievable by fair mechanisms for various classes of valuations besides additive ones. We first show that, for arbitrary $ε> 0$, every $(\frac{1}{2} + ε)$-EF1 mechanism for additive valuations admits an incentive ratio of at least $1.5$. Then, using the above lower bound for additive valuations in a black-box manner, we show that for arbitrary $ε> 0$, every $ε$-EF1 mechanism for cancelable valuations admits an infinite incentive ratio. Moreover, for subadditive cancelable valuations, we show that Round-Robin, which satisfies EF1, achieves an incentive ratio of $2$, and every $(φ- 1)$-EF1 mechanism admits an incentive ratio of at least $φ$ with $φ= (1 + \sqrt{5}) / 2 \approx 1.618$. Finally, for submodular valuations, we show that Round-Robin, which satisfies $\frac{1}{2}$-EF1, admits an incentive ratio of $n$.

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arXiv2024

A Complete Landscape for the Price of Envy-Freeness

We study the efficiency of fair allocations using the well-studied price of fairness concept, which quantitatively measures the worst-case efficiency loss when imposing fairness constraints. Previous works provided partial results on the price of fairness with well-known fairness notions such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). In this paper, we give a complete characterization for the price of envy-freeness in various settings. In particular, we first consider the two-agent case under the indivisible-goods setting and present tight ratios for the price of EF1 (for scaled utility) and EFX (for unscaled utility), which resolve questions left open in the literature. Next, we consider the mixed goods setting which concerns a mixture of both divisible and indivisible goods. We focus on envy-freeness for mixed goods (EFM), which generalizes both envy-freeness and EF1, as well as its strengthening called envy-freeness up to any good for mixed goods (EFXM), which generalizes envy-freeness and EFX. To this end, we settle the price of EFM and EFXM by providing a complete picture of tight bounds for two agents and asymptotically tight bounds for $n$ agents, for both scaled and unscaled utilities.

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arXiv2023

On the Existence of EFX (and Pareto-Optimal) Allocations for Binary Chores

We study the problem of allocating a group of indivisible chores among agents while each chore has a binary marginal. We focus on the fairness criteria of envy-freeness up to any item (EFX) and investigate the existence of EFX allocations. We show that when agents have additive binary cost functions, there exist EFX and Pareto-optimal (PO) allocations that can be computed in polynomial time. To the best of our knowledge, this is the first setting of a general number of agents that admits EFX and PO allocations, before which EFX and PO allocations have only been shown to exist for three bivalued agents. We further consider more general cost functions: cancelable and general monotone (both with binary marginal). We show that EFX allocations exist and can be computed for binary cancelable chores, but EFX is incompatible with PO. For general binary marginal functions, we propose an algorithm that computes (partial) envy-free (EF) allocations with at most $n-1$ unallocated items.

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