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21 pages, 2403 KB

Open AccessArticle

Blockchain-Enabled Data Supply Chain Governance: An Evolutionary Game Model Based on Prospect Theory

by Jie Zhang and Jian Yang

Mathematics 2026, 14(3), 432; https://doi.org/10.3390/math14030432 - 26 Jan 2026

With the continuous expansion of data trading, the data supply chain system has gradually developed and improved. However, frequent security issues during the data transaction process have seriously hindered the development of the digital economy. As a key link in the data supply [...] Read more.

With the continuous expansion of data trading, the data supply chain system has gradually developed and improved. However, frequent security issues during the data transaction process have seriously hindered the development of the digital economy. As a key link in the data supply chain, the data trading market needs to use blockchain technology to achieve full-chain supervision of the data supply chain, which has become a top priority. Based on prospect theory, this paper constructs an evolutionary game model composed of data suppliers, consumers and data trading markets at all levels. The main factors affecting the system game strategy are discussed. The results show that: (1) The development of the data supply chain system can be divided into three stages, and blockchain technology plays a key role in realizing full-chain supervision of the data transaction process. The costs of blockchain adoption, market rewards, and penalties significantly affect the behavior of all parties. (2) The behavior of data suppliers has strong negative externalities and affects other participants. In addition, the larger the size of the data transaction, the lower the probability of breach by the data provider. (3) Adopting blockchain technology and implementing effective incentives can promote the development of the data supply chain. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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42 pages, 3816 KB

Open AccessArticle

Dynamic Decision-Making for Resource Collaboration in Complex Computing Networks: A Differential Game and Intelligent Optimization Approach

by Cai Qi and Zibin Zhang

Mathematics 2026, 14(2), 320; https://doi.org/10.3390/math14020320 - 17 Jan 2026

Viewed by 214

Abstract

End–edge–cloud collaboration enables significant improvements in system resource utilization by integrating heterogeneous resources while ensuring application-level quality of service (QoS). However, achieving efficient collaborative decision-making in such architectures poses critical challenges within dynamic and complex computing network environments, including dynamic resource allocation, incentive [...] Read more.

End–edge–cloud collaboration enables significant improvements in system resource utilization by integrating heterogeneous resources while ensuring application-level quality of service (QoS). However, achieving efficient collaborative decision-making in such architectures poses critical challenges within dynamic and complex computing network environments, including dynamic resource allocation, incentive alignment between cloud and edge entities, and multi-objective optimization. To address these issues, this paper proposes a dynamic resource optimization framework for complex cloud–edge collaborative networks, decomposing the problem into two hierarchical decision schemes: cloud-level coordination and edge-side coordination, thereby achieving adaptive resource orchestration across the End–edge–cloud continuum. Furthermore, leveraging differential game theory, we model the dynamic resource allocation and cooperation incentives between cloud and edge nodes, and derive a feedback Nash equilibrium to maximize the overall system utility, effectively resolving the inherent conflicts of interest in cloud–edge collaboration. Additionally, we formulate a joint optimization model for energy consumption and latency, and propose an Improved Discrete Artificial Hummingbird Algorithm (IDAHA) to achieve an optimal trade-off between these competing objectives, addressing the challenge of multi-objective coordination from the user perspective. Extensive simulation results demonstrate that the proposed methods exhibit superior performance in multi-objective optimization, incentive alignment, and dynamic resource decision-making, significantly enhancing the adaptability and collaborative efficiency of complex cloud–edge networks. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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23 pages, 2058 KB

Open AccessArticle

On the Evolutionary Dynamics and Optimal Control of a Tripartite Game in the Pharmaceutical Procurement Supply Chain with Regulatory Participation

by Zhao Li and Yumu Wang

Mathematics 2026, 14(1), 56; https://doi.org/10.3390/math14010056 - 24 Dec 2025

Viewed by 324

Abstract

This study involves the construction of a dynamic evolutionary game model involving three key participants, including the Group Purchasing Organization (GPO), medical institutions, and pharmaceutical suppliers, while comprehensively considering critical factors such as benefit compensation, bad debt risk, and fiscal costs. The model [...] Read more.

This study involves the construction of a dynamic evolutionary game model involving three key participants, including the Group Purchasing Organization (GPO), medical institutions, and pharmaceutical suppliers, while comprehensively considering critical factors such as benefit compensation, bad debt risk, and fiscal costs. The model characterizes the strategy evolution of each participant under bounded rationality and imitation learning mechanisms. Based on the replicator dynamics equations, the evolutionary trajectories and equilibrium conditions of the three parties’ strategies are systematically derived. The Jacobian matrix is then used to analyze the local stability of eight boundary equilibria and potential internal mixed equilibria. Furthermore, to capture the optimal adjustment process of the compensation mechanism, the GPO’s compensation level is introduced into an optimal control framework. A controlled evolutionary system is formulated, and the dynamic optimal relationship between compensation intensity and system state is described using the Hamilton–Jacobi–Bellman (HJB) equation. Through analytical linearization and numerical simulations, the optimal feedback compensation law and its closed-loop evolutionary trajectory are obtained, allowing for a comparative analysis between the “fixed compensation” and “optimal compensation” scenarios. The results reveal that an appropriately designed dynamic compensation mechanism can significantly enhance system cooperation stability and overall social welfare. This provides a quantitative theoretical foundation and methodological tool for the refined design and dynamic regulation of pharmaceutical group purchasing policies. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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22 pages, 3335 KB

Open AccessArticle

Estimate Laplacian Spectral Properties of Large-Scale Networks by Random Walks and Graph Transformation

by Changlei Zhan, Xiangyu Li and Jie Chen

Mathematics 2026, 14(1), 26; https://doi.org/10.3390/math14010026 - 21 Dec 2025

Viewed by 262

Abstract

For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices [...] Read more.

For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices are also important for invariants of graphs. However, for large-scale networks, it is difficult to calculate eigenvalues of the Laplacian matrix directly because it is either very difficult to obtain the whole network structure or requires a lot of computing resources. Therefore, this article makes the following contributions. Firstly, this paper proposes a random walk approach for estimating the bounds of the greatest eigenvalues of Laplacian matrices for large-scale networks. Considering the relationship between the spectral moments of the adjacency matrix and the closed paths in the network, we utilize the relationship between the adjacency matrix and the Laplacian matrix to establish the relationship between the Laplacian matrix and the closed paths. Then, we employ equiprobable random walks to sample the large graph to obtain the small graph. Through algebraic topology knowledge, we obtain the bounds of the largest eigenvalue of the Laplacian matrix of the large graph by using Laplacian spectral moments of the small graph. Secondly, for high-order networks, this paper proposes a method based on random walks and graph transformations. The graph transformation we propose mainly converts graphs with second-order simplices into ordinary weighted graphs, thereby transforming the problem of solving the spectral moments of the second-order combined Laplacian matrix into solving the spectral moments of the adjacency matrix. Then, we use the aforementioned random walk method to solve bounds of the greatest eigenvalue of the second-order combinatorial Laplacian matrix. Finally, by comparing the proposed method with existing algorithms in synthetic and real networks, its accuracy and superiority are demonstrated. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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22 pages, 2219 KB

Open AccessArticle

How Does Government Innovation Regulation Inhibit Corporate “Greenwashing”?—Based on a Tripartite Evolutionary Game Perspective

by Yuqing Zhu, Mengyun Wu, Jie Lu and Qi Jiang

Mathematics 2025, 13(22), 3658; https://doi.org/10.3390/math13223658 - 14 Nov 2025

Viewed by 547

Abstract

A strategic fulcrum for leading high-quality economic development and shaping the nation’s future. Core competitiveness lies in how governments can effectively stimulate consumer demand for green consumption and motivate enterprises to pursue green technology innovation through the development of precise and efficient innovative [...] Read more.

A strategic fulcrum for leading high-quality economic development and shaping the nation’s future. Core competitiveness lies in how governments can effectively stimulate consumer demand for green consumption and motivate enterprises to pursue green technology innovation through the development of precise and efficient innovative regulation models. In this paper, a tripartite evolutionary game model is constructed based on evolutionary game theory, encompassing the government, enterprises, and consumers. We analyze the strategic interactions and evolutionary path among these three entities under conditions of bounded rationality and information asymmetry. The research reveals the following: (1) the government can effectively guide enterprises towards genuine green innovation through enhanced rewards for substantive innovation and increased penalties for strategic innovation; (2) consumer purchasing decisions are significantly shaped by economic benefits, perceived social value, and government subsidies, with their market choices forming a critical external supervisory force; and (3) government regulatory strategies are dynamically adjusted in response to market integrity levels and social welfare, with a tendency to implement innovative regulation when “greenwashing” risk is elevated. In conclusion, simulation analysis is conducted using MATLAB 2018a, and governance recommendations are offered based on three dimensions: precise government regulation, enhanced corporate responsibility, and enhanced consumer capabilities. These recommendations offer both a theoretical basis and a practical path for establishing an integrated green innovation governance system based on incentive constraint empowerment. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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21 pages, 4923 KB

Open AccessArticle

Dynamic Analysis of China’s Urban Economic Spatial Network and Its Multidimensional Impact on Building Carbon Emissions

by Juan Li and Mei Sun

Mathematics 2025, 13(21), 3415; https://doi.org/10.3390/math13213415 - 27 Oct 2025

Cited by 1 | Viewed by 530

Abstract

With the continuous development of cities, the network connections between Chinese cities have rapidly strengthened, and cities are gradually transforming from traditional production bases into economic platforms within dynamic spaces. In this process, urban building carbon emissions are not only determined by the [...] Read more.

With the continuous development of cities, the network connections between Chinese cities have rapidly strengthened, and cities are gradually transforming from traditional production bases into economic platforms within dynamic spaces. In this process, urban building carbon emissions are not only determined by the city’s own resource and industrial advantages but are increasingly influenced by its position within the urban economic space network. This study constructs an urban economic spatial network using the gravity model, and based on dynamic data of building carbon emissions in Chinese cities from 2008 to 2020, develops a new analytical framework from the perspective of dynamic network evolution to examine the impact mechanisms of urban network position and residential activity intensity on building carbon emissions. The findings indicate that both residents’ activity intensity and city’s network position have a significant positive impact on per capita building carbon emissions, The impact coefficient between residential activity intensity and per capita building carbon emissions is 0.278 (p < 0.01). This conclusion remains valid after robustness and endogeneity tests. The city’s network position can mitigate the detrimental impact that residents’ activity intensity has on per capita building carbon emissions, particularly in the dynamic decision-making process, where cities can adjust their strategies based on their network position. The influence of city’s network position on per capita building carbon emissions exhibits multidimensional heterogeneity, with its effect being more significant in megalopolis and metropolis compared to large city and medium & small city. Specifically, in megalopolis, the network position impact coefficient is 0.22, significantly higher than 0.039 in medium & small city. These findings provide new perspectives for reducing building carbon emissions at the urban-level in the context of dynamic spatial mobility. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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11 pages, 285 KB

Open AccessArticle

Toward a Distributed Potential Game Optimization to Sensor Area Coverage Problem

by Jun Huang, Jie Chen, Rongcheng Dong, Xinli Xiong and Simao Xu

Mathematics 2025, 13(17), 2709; https://doi.org/10.3390/math13172709 - 22 Aug 2025

Viewed by 630

Abstract

The sensor coverage problem is a well-known combinatorial optimization problem that continues to attract the attention of many researchers. The existing game-based algorithms mainly pursue a feasible solution when solving this problem. This problem is described as a potential game, and a memory-based [...] Read more.

The sensor coverage problem is a well-known combinatorial optimization problem that continues to attract the attention of many researchers. The existing game-based algorithms mainly pursue a feasible solution when solving this problem. This problem is described as a potential game, and a memory-based greedy learning (MGL) algorithm is proposed, which can ensure convergence to Nash equilibrium. Compared with existing representative algorithms, our proposed algorithm performs the best in terms of average coverage, best value, and standard deviation within within a suitable time. In addition, increasing memory length helps to generate a better Nash equilibrium. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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15 pages, 656 KB

Open AccessArticle

Green Technology Game and Data-Driven Parameter Identification in the Digital Economy

by Xiaofeng Li and Qun Zhao

Mathematics 2025, 13(14), 2302; https://doi.org/10.3390/math13142302 - 18 Jul 2025

Viewed by 600

Abstract

The digital economy presents multiple challenges to the promotion of green technologies, including behavioral uncertainty among firms, heterogeneous technological choices, and disparities in policy incentive strength. This study develops a tripartite evolutionary game model encompassing government, production enterprises, and technology suppliers to systematically [...] Read more.

The digital economy presents multiple challenges to the promotion of green technologies, including behavioral uncertainty among firms, heterogeneous technological choices, and disparities in policy incentive strength. This study develops a tripartite evolutionary game model encompassing government, production enterprises, and technology suppliers to systematically explore the strategic evolution mechanisms underlying green technology adoption. A three-dimensional nonlinear dynamic system is constructed using replicator dynamics, and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is applied to identify key cost and benefit parameters for firms. Simulation results exhibit a strong match between the estimated parameters and simulated data, highlighting the model’s identifiability and explanatory capacity. In addition, the stability of eight pure strategy equilibrium points is examined through Jacobian analysis, revealing the evolutionary trajectories and local stability features across various strategic configurations. These findings offer theoretical guidance for optimizing green policy design and identifying behavioral pathways, while establishing a foundation for data-driven modeling of dynamic evolutionary processes. Full article

(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)

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