arXiv subjects

Qizhi Fang

Publications and source records attributed to Qizhi Fang.

At least 19 recordsLinked to original sources

arXiv2026

Flow Games with Public Arcs: the Least Core and the Nucleolus

We study flow games with public arcs, an extension of classical cooperative flow games that allows players to use public resources. In these games, a coalition corresponds to a set of arcs, while certain arcs, called public arcs, can be used freely by any coalition. The value of a coalition is the maximum flow value achievable using the arcs controlled by the coalition along with the public arcs. We investigate two solution concepts, the least core and the nucleolus. Both solution concepts provide fair ways to allocate the value of the grand coalition among individual players. We provide polynomial-size formulations of the least core of these games. We also give a deterministic polynomial-time algorithm for computing the nucleolus, whether or not the core is empty.

econ.TH↗

arXiv2026

Mechanism Design for Facility Location Games Under a Prelocated Facility

We study the problem of locating a new homogeneous facility under a prelocated facility. Here, a set of $n$ agents is located on a real line or a circle, each of whom has her location as private information, and her cost is the (expected) distance from her location to the nearest facility. Our goal is to design mechanisms which can approximately minimize the maximum cost or the social cost while eliciting agents' private information truthfully (i.e., strategy-proof). Based on real-life scenarios, we consider the problem in two settings: the general setting where each agent can be located at both sides of the prelocated facility, and the special setting where all the agents are located at the same side of the prelocated facility. For agents on a line, in the general setting, we design the best possible deterministic strategy-proof mechanism with $2$-approximation and provide a lower bound of $1.5-ε\textbf{ }(ε>0)$ for any randomized strategy-proof mechanism under the maximum cost objective. For the social cost, we obtain an upper bound of $n$ for deterministic strategy-proof mechanisms and lower bounds of $1.5$ and $1.0425$ for any deterministic strategy-proof mechanism and any randomized strategy-proof mechanism, respectively. In the special setting, we further provide a randomized strategy-proof $5/3$-approximation mechanism for the maximum cost and a deterministic strategy-proof $(n-1)$-approximation mechanism for the social cost. For agents on a circle, we provide a deterministic strategy-proof 2-approximation mechanism under the maximum cost objective.

cs.GT↗

arXiv2026

Constrained Distributed Heterogeneous Two-Facility Location Problems with Max-Variant Cost

This paper investigates a constrained distributed heterogeneous two-facility location problem under the max-variant cost model. In this setting, a set of agents with private locations on the real line is partitioned into disjoint groups. The constraint stipulates that facilities must be situated within a given multiset of candidate locations, with the restriction that each candidate location can host at most one facility. Under the max-variant model, an agent's individual cost is defined as the distance from their location to the farthest facility. Our objective is to design strategyproof distributed mechanisms that incentivize agents to report their locations truthfully while approximating social objectives. Such mechanisms operate in two stages: first, for each group, a pair of candidate locations is selected as representatives based solely on local reports; subsequently, the mechanism outputs two final facility locations from the set of all representatives. We focus on a class of deterministic strategyproof distributed mechanisms and establish constant lower and upper bounds on the distortion under four social objectives: Average-of-Average, Max-of-Max, Average-of-Max, and Max-of-Average costs.

cs.GT↗

arXiv2026

Mechanism Design for Locating a Bridge Between Regions with Prelocated Facilities

In many urban planning projects, social planners require the construction of a bridge to connect two regions separated by obstacles such as rivers or highways. This paper studies the mechanism design problem for locating a bridge between two separate regions, each of which has been equipped with a facility. There are a set of agents located in each region and each agent has her location as private information. Once the bridge is built, the agents will go to the nearest facility to receive service and each agent's cost is the distance from her location to the nearest prelocated facility via the bridge. We investigate social cost and maximum cost under strategyproof (SP) mechanisms, with stronger notions of group-strategyproof (GSP) and strong group-strategyproof (SGSP). For the maximum cost objective, we characterize the optimal solution and show that it satisfies GSP. Under the SGSP, we propose a deterministic 3-approximation mechanism and a randomized 2-approximation mechanism, while proving a lower bound of 2 for any deterministic SGSP mechanism. For the social cost objective, we present a deterministic 3-approximation mechanism and a randomized 2-approximation mechanism that satisfy GSP. We establish lower bounds of 2 and 1.1 for deterministic and randomized SP mechanisms, respectively. Under the SGSP, the lower bound for deterministic mechanisms increases to 1 + min{m, n}, and we provide a (1 + 2 min{m, n})-approximation mechanism. For randomized mechanisms, the lower bound remains 1.1, while an upper bound of (1 + 2mn/(m+n)) is achieved.

cs.GT↗

arXiv2026

Facility Location Game with Envy Ratio

We study the one-facility location game on a real line with a new objective called envy ratio. The envy ratio, which is adopted from fair division and represents the egalitarianism, is defined as the maximum over the ratios between any two agents' utilities. We are interested in strategyproof or group strategyproof mechanisms that can minimize the envy ratio objective. We consider the model in two settings that can capture natural scenarios: the facility location and all the agents' locations are restricted on a fixed interval; every agent's location can be any point on the real line but the facility location is restricted on a relative interval. In both settings, we obtain the optimal solution and the best deterministic strategyproof mechanism which is also group strategyproof. In the first setting, we provide a lower bound for randomized strategyproof mechanisms. In the second setting, we give a lower bound and two upper bounds for randomized strategyproof mechanisms.

cs.GT↗

arXiv2026

A Complete Characterization of Convexity in Flow Games

Flow games coincide precisely with the fundamental class of non-negative totally balanced games. However, the conditions for their convexity have remained elusive. In this paper, we resolve this challenge by providing a complete characterization. Specifically, we show that a flow game is convex if and only if its underlying network satisfies three structural conditions: acyclicity, bottleneck exclusivity, and capacity sufficiency. These structural conditions are also equivalent to dual separability, which resolves the apparent paradox between cycle orientations and game-theoretic convexity by decoupling path contributions via bottleneck exclusivity. Furthermore, our characterization yields an efficient recognition procedure, establishing that flow game convexity is verifiable in polynomial time.

cs.GT↗

arXiv2026

Full characterization of core for nonlinear optimization games

We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands the scope of cooperative games that can be analyzed and contributes to the literature on games induced from optimization models. We apply these insights to not only establish connections with and provide new insights on classical models but also solve new games untamed in the existing literature, including combinatorial quadratic and ratio games such as portfolio, maximum cut, matching, and assortment games. These results are further extended to more general models and also the approximate core.

math.OC↗

arXiv2025

Facility Location Games for Multi-Location Agents with Satisfaction

In this paper, we study mechanism design for single-facility location games where each agent has multiple private locations in [0, 1]. The individual objective is a satisfaction function that measures the discrepancy between the optimal facility location for an agent and the location provided by the mechanism. Based on different distance functions from agents to the facility, we consider two types of individual objectives: the sum-variant satisfaction and the max-variant satisfaction. Our goal is to design mechanisms that locate one facility to maximize the sum (or the minimum) of all agents' satisfactions, while incentivizing agents to truthfully report their locations. In this paper, we mainly focus on desirable and obnoxious facility location games. For desirable facility location games, we propose two group strategy-proof mechanisms with approximation ratios of 2 and 5/4 for maximizing the sum of the sum-variant and max-variant satisfaction, respectively. Moreover, another mechanism achieves an approximation ratio of 2 for simultaneously maximizing the minimum of the sum-variant satisfaction and the minimum of the max-variant satisfaction. For obnoxious facility location games, we establish that two group strategy-proof mechanisms are the best possible, providing an approximation ratio of 2 for maximizing the sum of the sum-variant satisfaction and the sum of the max-variant satisfaction, respectively. Additionally, we devise two 4/3-approximation randomized group strategy-proof mechanisms, and provide two lower bounds of 1.0625 and 1.0448 of randomized strategy-proof mechanisms for maximizing the sum of the sum-variant satisfaction and the sum of the max-variant satisfaction, respectively.

cs.GT↗

arXiv2025

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint

In this paper, we study a truthful two-obnoxious-facility location problem, in which each agent has a private location in [0, 1] and a public optional preference over two obnoxious facilities, and there is a minimum distance constraint d between the two facilities. Each agent wants to be as far away as possible from the facilities that affect her, and the utility of each agent is the total distance from her to these facilities. The goal is to decide how to place the facilities in [0, 1] so as to incentivize agents to report their private locations truthfully as well as maximize the social utility. First, we consider the special setting where d = 0, that is, the two facilities can be located at any point in [0, 1]. We propose a deterministic strategyproof mechanism with approximation ratio of at most 4 and a randomized strategyproof mechanism with approximation ratio of at most 2, respectively. Then we study the general setting. We propose a deterministic strategyproof mechanism with approximation ratio of at most 8 and a randomized strategyproof mechanism with approximation ratio of at most 4, respectively. Furthermore, we provide lower bounds of 2 and 14/13 on the approximation ratio for any deterministic and any randomized strategyproof mechanism, respectively.

cs.GT↗

arXiv2025

Constrained Distributed Heterogeneous Two-Facility Location Problems with Max-Variant Cost

We study a constrained distributed heterogeneous two-facility location problem, where a set of agents with private locations on the real line are divided into disjoint groups. The constraint means that the facilities can only be built in a given multiset of candidate locations and at most one facility can be built at each candidate location. Given the locations of the two facilities, the cost of an agent is the distance from her location to the farthest facility (referred to as max-variant). Our goal is to design strategyproof distributed mechanisms that can incentivize all agents to truthfully report their locations and approximately optimize some social objective. A distributed mechanism consists of two steps: for each group, the mechanism chooses two candidate locations as the representatives of the group based only on the locations reported by agents therein; then, it outputs two facility locations among all the representatives. We focus on a class of deterministic strategyproof distributed mechanisms and analyze upper and lower bounds on the distortion under the Average-of-Average cost (average of the average individual cost of agents in each group), the Max-of-Max cost (maximum individual cost among all agents), the Average-of-Max cost (average of the maximum individual cost among all agents in each group) and the Max-of-Average cost (maximum of the average individual cost of all agents in each group). Under four social objectives, we obtain constant upper and lower distortion bounds.

cs.GT↗

arXiv2025

On the Approximate Core and Nucleon of Flow Games with Public Arcs

We investigate flow games featuring both private arcs owned by individual players and public arcs accessible cost-free to all coalitions. We explore two solution concepts within this framework: the approximate core and the nucleon. The approximate core relaxes core requirements by permitting a bounded relative payoff deviation for every coalition, and the nucleon is a multiplicative analogue of Schmeidler's nucleolus which lexicographically maximizes the vector consisting of relative payoff deviations for every coalition arranged in a non-decreasing order. By leveraging a decomposition property for paths and cycles in a flow network, we derive complete characterizations for the approximate core and demonstrate that the nucleon can be computed in polynomial time.

cs.GT↗

arXiv2023

Approximate Core Allocations for Edge Cover Games

We study the approximate core for edge cover games, which are cooperative games stemming from edge cover problems. In these games, each player controls a vertex on a network $G = (V, E; w)$, and the cost of a coalition $S\subseteq V$ is equivalent to the minimum weight of edge covers in the subgraph induced by $S$. We prove that the 3/4-core of edge cover games is always non-empty and can be computed in polynomial time by using linear program duality approach. This ratio is the best possible, as it represents the integrality gap of the natural LP for edge cover problems. Moreover, our analysis reveals that the ratio of approximate core corresponds with the length of the shortest odd cycle of underlying graphs.

math.CO↗

arXiv2022

Constrained Heterogeneous Two-facility Location Games with Max-variant Cost

In this paper, we propose a constrained heterogeneous facility location model where a set of alternative locations are feasible for building facilities and the number of facilities built at each location is limited. Supposing that a set of agents on the real line can strategically report their locations and each agent's cost is her distance to the further facility that she is interested in, we study deterministic mechanism design without money for constrained heterogeneous two-facility location games. Depending on whether agents have optional preference, the problem is considered in two settings: the compulsory setting and the optional setting. In the compulsory setting where each agent is served by the two heterogeneous facilities, we provide a 3-approximate deterministic group strategyproof mechanism for the sum/maximum cost objective respectively, which is also the best deterministic strategyproof mechanism under the corresponding social objective. In the optional setting where each agent can be interested in one of the two facilities or both, we propose a deterministic group strategyproof mechanism with approximation ratio of at most $2n+1$ for the sum cost objective and a deterministic group strategyproof mechanism with approximation ratio of at most 9 for the maximum cost objective.

cs.GT↗

arXiv2022

Arboricity games: the core and the nucleolus

The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We introduce the arboricity game as a cooperative cost game defined on a graph. The players are edges, and the cost of each coalition is the arboricity of the subgraph induced by the coalition. We study properties of the core and propose an efficient algorithm for computing the nucleolus when the core is not empty. In order to compute the nucleolus in the core, we introduce the prime partition which is built on the densest subgraph lattice. The prime partition decomposes the edge set of a graph into a partially ordered set defined from minimal densest minors and their invariant precedence relation. Moreover, edges from the same partition always have the same value in a core allocation. Consequently, when the core is not empty, the prime partition significantly reduces the number of variables and constraints required in the linear programs of Maschler's scheme and allows us to compute the nucleolus in polynomial time. Besides, the prime partition provides a graph decomposition analogous to the celebrated core decomposition and the density-friendly decomposition, which may be of independent interest.

cs.GT↗

arXiv2021

Approximate Core Allocations for Multiple Partners Matching Games

The matching game is a cooperative game where the value of every coalition is the maximum revenue of players in the coalition can make by forming pairwise disjoint partners. The multiple partners matching game generalizes the matching game by allowing each player to have more than one possibly repeated partner. In this paper, we study profit-sharing in multiple partners matching games. A central concept for profit-sharing is the core which consists of all possible ways of distributing the profit among individual players such that the grand coalition remains intact. The core of multiple partners matching games may be empty [Deng et al., Algorithmic aspects of the core of combinatorial optimization games, Math. Oper. Res., 1999.]; even when the core is non-empty, the core membership problem is intractable in general [Biro et al., The stable fixtures problem with payments, Games Econ. Behav., 2018]. Thus we study approximate core allocations upon which a coalition may be paid less than the profit it makes by seceding from the grand coalition. We provide an LP-based mechanism guaranteeing that no coalition is paid less than $2/3$ times the profit it makes on its own. We also show that $2/3$ is the best possible factor relative to the underlying LP-relaxation. Our result generalizes the work of Vazirani [Vazirani, The general graph matching game: approximate core, arXiv, 2021] from matching games to multiple partners matching games.

cs.GT↗

arXiv2021

Population Monotonicity in Matching Games

A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population monotonic allocation scheme is a collection of rules defining how to share the profit among players in each coalition such that every player is better off when the coalition expands. In this paper, we study matching games and provide a necessary and sufficient characterization for the existence of population monotonic allocation schemes. Our characterization also implies that whether a matching game admits population monotonic allocation schemes can be determined efficiently.

cs.GT↗

arXiv2021

A Random Algorithm for Profit Maximization with Multiple Adoptions in Online Social Networks

Online social networks have been one of the most effective platforms for marketing and advertising. Through "word of mouth" effects, information or product adoption could spread from some influential individuals to millions of users in social networks. Given a social network $G$ and a constant $k$, the influence maximization problem seeks for $k$ nodes in $G$ that can influence the largest number of nodes. This problem has found important applications, and a large amount of works have been devoted to identifying the few most influential users. But most of existing works only focus on the diffusion of a single idea or product in social networks. However, in reality, one company may produce multiple kinds of products and one user may also have multiple adoptions. Given multiple kinds of different products with different activation costs and profits, it is crucial for the company to distribute the limited budget among multiple products in order to achieve profit maximization. Profit Maximization with Multiple Adoptions (PM$^{2}$A) problem aims to seek for a seed set within the budget to maximize the overall profit. In this paper, a Randomized Modified Greedy (RMG) algorithm based on the Reverse Influence Sampling (RIS) technique is presented for the PM$^{2}$A problem, which could achieve a $(1-1/e-\varepsilon)$-approximate solution with high probability. Compared with the algorithm proposed in [16] that achieves a $\frac{1}{2}(1-1/e^{2})$-approximate solution, our algorithm provides a better performance ratio which is also the best performance ratio of the PM$^{2}$A problem. Comprehensive experiments on three real-world social networks are conducted, and the results demonstrate that our RMG algorithm outperforms the algorithm proposed in [16] and other heuristics in terms of profit maximization, and could better allocate the budget.

cs.SI↗

arXiv2020

On the Convexity of Independent Set Games

Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the convexity of independent set games, as convex games possess many nice properties both economically and computationally. For independent set games introduced by Deng et al. (Math. Oper. Res., 24:751-766, 1999), we provide a necessary and sufficient characterization for the convexity, i.e., every non-pendant edge is incident to a pendant edge in the underlying graph. Our characterization immediately yields a polynomial time algorithm for recognizing convex instances of independent set games. Besides, we introduce a new class of independent set games and provide an efficient characterization for the convexity.

cs.DM↗