arXiv subjects

Gehui Xu

Publications and source records attributed to Gehui Xu.

16 recordsLinked to original sources

arXiv2026

When Does Selfishness Align with Team Goals? A Structural Analysis of Equilibrium and Optimality

This paper investigates the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of self-interested decisions on team performance. In classical team decision problems, team members typically act cooperatively towards a common objective to achieve a team-optimal solution. However, in practice, members may behave selfishly by prioritizing their goals, resulting in an NE under a non-cooperative game. To study this misalignment, we develop a parameterized model for team and game problems, where game parameters represent each individual's deviation from the team objective. The study begins by exploring the consistency and deviation between the NE and the team-optimal solution under fixed game parameters. We provide a necessary and sufficient condition for any NE to be a team optimum, along with establishing an upper bound to measure their difference when this consistency fails. We then study how to steer the NE toward the team-optimal solution by adjusting game parameters in an incomplete-information leader--follower setting, where the leader observes only equilibrium responses rather than the exact lower-level game structure. To address this challenge, we develop a two-stage learned-response intervention framework: the leader first learns a behaviorally consistent lower-level model from observed equilibria and then computes the intervention over the learned response map using bilevel hypergradient optimization, followed by convergence analysis and simulation validation.

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arXiv2026

Deception Equilibrium Analysis for Three-Party Stackelberg Game with Insider

This paper investigates strategic interactions within a three party deception security game involving a defender, an insider, and external attackers. We propose a robust deception mechanism where the leader manipulates game parameters perceived by followers to enhance defense performance when followers operate under misperceived and uncertain observation. Specifically, we propose a unified three party leader follower game framework and introduce the concepts of Deception Stackelberg equilibria (DSE) and Hyper Nash equilibria (HNE), which generalize classical two-player Stackelberg and deception games. We develop necessary and sufficient conditions for the consistency between DSE and HNE, ensuring that the defender's utility remains invariant when the hierarchical structure degenerates into a simultaneous-move scenario. Moreover, we propose a scalable hypergradient-based algorithm with established convergence guarantees for seeking DSE, efficiently addressing the computational challenges posed by non-smooth and set-valued best-response mappings. Finally, we apply theoretical analysis to practical scenarios in secure wireless communication and defense against insider-assisted false data injection attacks.

cs.GT↗

arXiv2026

A Functional Learning Approach for Team-Optimal Traffic Coordination

In this paper, we develop a kernel-based policy iteration functional learning framework for computing team-optimal strategies in traffic coordination problems. We consider a multi-agent discrete-time linear system with a cost function that combines quadratic regulation terms and nonlinear safety penalties. Building on the Hilbert space formulation of offline receding-horizon policy iteration, we seek approximate solutions within a reproducing kernel Hilbert space, where the policy improvement step is implemented via a discrete Fréchet derivative. We further study the model-free receding-horizon scenario, where the system dynamics are estimated using recursive least squares, followed by updating the policy using rolling online data. The proposed method is tested in signal-free intersection scenarios via both model-based and model-free simulations and validated in SUMO.

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arXiv2026

Adaptive Mitigation of Insider Threats via Off-Policy Learning

An insider is a team member who covertly deviates from the team's optimal collaborative strategy to pursue a private objective while still appearing cooperative. Such an insider may initially behave cooperatively but later switch to selfish or malicious actions, thereby degrading collective performance, threatening mission success, and compromising operational safety. In this paper, we study such insider threats within an insider-aware, game-theoretic formulation, where the insider interacts with a decision maker (DM) under a continuous-time switched system, with each time interval characterized by a distinct insider behavioral pattern or threat level. We develop a periodic off-policy mitigation scheme that enables the DM to learn optimal mitigation policies from online data when encountering different insider threats, without requiring a priori knowledge of insider intentions. By designing appropriate conditions on the inter-learning interval time, we establish convergence guarantees for both the learning process and the closed-loop system, and characterize the corresponding mitigation performance achieved by the DM.

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arXiv2025

Game-Theoretic Learning-Based Mitigation of Insider Threats

An insider is defined as a team member who covertly deviates from the team's optimal collaborative control strategy in pursuit of a private objective, while maintaining an outward appearance of cooperation. Such insider threats can severely undermine cooperative systems: subtle deviations may degrade collective performance, jeopardize mission success, and compromise operational safety. This paper presents a comprehensive framework for identifying and mitigating insider threats in cooperative control settings. We introduce an insider-aware, game-theoretic formulation in which the insider's hidden intention is parameterized, allowing the threat identification task to be reformulated as a parameter estimation problem. To address this challenge, we employ an online indirect dual adaptive control approach that simultaneously infers the insider's control strategy and counteracts its negative influence. By injecting properly designed probing signals, the resulting mitigation policy asymptotically recovers the nominal optimal control law - one that would be achieved under full knowledge of the insider's objective. Simulation results validate the effectiveness of the proposed identification-mitigation framework and illustrate its capability to preserve team performance even in the presence of covert adversarial behavior.

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arXiv2025

Deviation Between Team-Optimal Solution and Nash Equilibrium in Flow Assignment Problems

We investigate the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of strategy deviation on team performance. As a working use case, we focus on a class of flow assignment problems in which each source node acts as a cooperating decision maker (DM) within a team that minimizes the team cost based on the team-optimal strategy. In practice, some selfish DMs may prioritize their own marginal cost and deviate from NE strategies, thus potentially degrading the overall performance. To quantify this deviation, we explore the deviation bound between the team-optimal solution and the NE in two specific scenarios: (i) when the team-optimal solution is unique and (ii) when multiple solutions do exist. This helps DMs analyze the factors influencing the deviation and adopting the NE strategy within a tolerable range. Furthermore, in the special case of a potential game model, we establish the consistency between the team-optimal solution and the NE. Once the consistency condition is satisfied, the strategy deviation does not alter the total cost, and DMs do not face a strategic trade-off. Finally, we validate our theoretical analysis through some simulation studies.

cs.GT↗

arXiv2025

Routing Guidance for Emerging Transportation Systems with Improved Dynamic Trip Equity

This paper presents a dynamic routing guidance system that optimizes route recommendations for individual vehicles in an emerging transportation system while enhancing travelers' trip equity. We develop a framework to quantify trip quality and equity in dynamic travel environments, providing new insights into how routing guidance influences equity in road transportation. Our approach enables real-time routing by incorporating both monitored and anticipated traffic congestion. We provide conditions that ensure perfect trip equity for all travelers in a free-flow network. Simulation studies on 1,000 vehicles traversing an urban road network in Boston demonstrate that our method improves trip equity by approximately 11.4\% compared to the shortest-route strategy. In addition, the results reveal that our approach redistributes travel costs across vehicle types through route optimization, contributing to a more equitable transportation system.

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arXiv2024

A Multi-Player Potential Game Approach for Sensor Network Localization with Noisy Measurements

Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.

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arXiv2024

Non-convex potential games for finding global solutions to sensor network localization

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

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arXiv2024

Inverse learning of black-box aggregator for robust Nash equilibrium

In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach.

cs.GT↗

arXiv2024

Global solution to sensor network localization: A non-convex potential game approach and its distributed implementation

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem.

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arXiv2023

Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the non-convexity, obtaining the existence condition of global NE is challenging, let alone designing theoretically guaranteed realization algorithms. This paper takes conjugate transformation to the formulation of non-convex multi-player games, and casts the complementary problem into a variational inequality (VI) problem with a continuous pseudo-gradient mapping. We then prove the existence condition of global NE: the solution to the VI problem satisfies a duality relation. Based on this VI formulation, we design a conjugate-based ordinary differential equation (ODE) to approach global NE, which is proved to have an exponential convergence rate. To make the dynamics more implementable, we further derive a discretized algorithm. We apply our algorithm to two typical scenarios: multi-player generalized monotone game and multi-player potential game. In the two settings, we prove that the step-size setting is required to be $\mathcal{O}(1/k)$ and $\mathcal{O}(1/\sqrt k)$ to yield the convergence rates of $\mathcal{O}(1/ k)$ and $\mathcal{O}(1/\sqrt k)$, respectively. Extensive experiments in robust neural network training and sensor localization are in full agreement with our theory.

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arXiv2022

Coincidence analysis of Stackelberg and Nash equilibria in three-player leader-follower security games

There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in practice due to subjective or objective factors, and then the Nash equilibrium (NE) strategy may be an alternative option. In this case, the leader may face a dilemma of choosing an SE strategy or an NE strategy. In this paper, we focus on a unified three-player leader-follower security game and study the coincidence between SE and NE. We first explore a necessary and sufficient condition for the case that each SE is an NE, which can be further presented concisely when the SE is unique. This condition not only provides access to seek a satisfactory SE strategy but also makes a criterion to verify an obtained SE strategy. Then we provide another appropriate condition for the case that at least one SE is an NE. Moreover, since the coincidence condition may not always be satisfied, we describe the closeness between SE and NE, and give an upper bound of their deviation. Finally, we show the applicability of the obtained theoretical results in several practical security cases, including the secure transmission problem and the cybersecurity defense.

cs.GT↗

arXiv2022

Algorithm design and approximation analysis on distributed robust game

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst case. However, it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets, which may not have analytic expressions or are endowed with high-dimensional nonlinearities. To solve this problem, we first approximate parameter sets with inscribed polyhedrons, and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization. Then we propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces an $ε$-generalized Nash equilibrium of the original game, followed by convergence analysis. Moreover, resorting to the metric spaces and the analysis on nonlinear perturbed systems, we estimate the approximation accuracy related to $ε$ and point out the factors influencing the accuracy of $ε$.

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arXiv2021

Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization

To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed projection-based algorithms. In fact, our continuous-time algorithm well inherits good capabilities of mirror descent approaches to rapidly compute explicit solutions to the problems with some specific constraint structures. Moreover, we rigorously prove the convergence of our algorithm, along with the boundedness of the trajectory and the accuracy of the solution.

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arXiv2021

Efficient algorithm for approximating Nash equilibrium of distributed aggregative games

In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the Nash equilibrium of the approximate game is the $ε$-Nash equilibrium of the original game, and then propose a distributed algorithm to seek the $ε$-Nash equilibrium, where the projection is then of a standard form in quadratic programming. With the help of the existing developed methods for solving quadratic programming, we show the convergence of the proposed algorithm, and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to $ε$. Additionally, we investigate the computational cost saved by approximation on numerical examples.

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