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Advances in Complex Systems and Evolutionary Game Theory
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Advances in Complex Systems and Evolutionary Game Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (15 November 2023) | Viewed by 11364

Special Issue Editors

Prof. Dr. Chengyi Xia

E-Mail Website
Guest Editor
School of Control Science and Engineering, Tiangong University, Tianjin 300387, China
Interests: complex systems; complex networks; evolutionary game theory; computational complexity; Monte Carlo methods; discrete event systems; social network theory
Dr. Changwei Huang

E-Mail Website
Guest Editor
School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China
Interests: evolutionary game theory; complex networks; complex systems; opinion dynamics; social behavior; social networks; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the rapid development of network science, complex networks have become an important method and tool to describe the interactions among individuals within complex systems. On the one hand, many complex systems in nature and society could be considered as networks composed of interacting units and analyzed by statistical physics methods. On the other hand, the mechanisms of the spontaneous emergence and maintenance of cooperative behavior among selfish individuals have attracted continuous attention over the past several decades, among which evolutionary game theory provides a powerful theoretical framework to address them. Although tremendous efforts have been put into explaining and understanding how altruistic cooperation can evolve in the situation of social dilemmas, the evolution of collective cooperation is still under-researched, and is one of 125 scientific puzzles to be resolved urgently, as proposed by Science magazine in 2005.

This Special Issue focuses on the advances in complex systems and evolutionary game theory. We are looking for original papers with novel research contributions in all aspects of the dynamical analysis of complex systems and evolutionary game dynamics. Topics of interest include, but are not limited to:

  • Complex network modeling;
  • Complex system modeling;
  • Network science;
  • Dynamical analysis of complex networks;
  • Evolutionary game dynamics: theory, modeling and application;
  • Evolution of cooperation: experimental evidence;
  • Mechanisms triggering cooperative evolution in social dilemmas;
  • The application of complex system theory to multidisciplinary fields.

Prof. Dr. Chengyi Xia
Dr. Changwei Huang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex systems
  • complex networks
  • multi-agent systems
  • social networks
  • spreading processes over networks
  • evolutionary games
  • cooperative behaviors
  • network science
  • graph theory
  • evolutionary dynamics
  • collective cooperation
  • nonlinear dynamics
  • cooperation
  • social dynamics

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Published Papers (7 papers)

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Research

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18 pages, 1173 KiB  
Article
Evolutionary Game Analysis of Digital Financial Enterprises and Regulators Based on Delayed Replication Dynamic Equation
by Mengzhu Xu, Zixin Liu, Changjin Xu and Nengfa Wang
Mathematics 2024, 12(3), 385; https://doi.org/10.3390/math12030385 - 24 Jan 2024
Cited by 1 | Viewed by 1049
Abstract
With the frequent occurrence of financial risks, financial innovation supervision has become an important research issue, and excellent regulatory strategies are of great significance to maintain the stability and sustainable development of financial markets. Thus, this paper intends to analyze the financial regulation [...] Read more.
With the frequent occurrence of financial risks, financial innovation supervision has become an important research issue, and excellent regulatory strategies are of great significance to maintain the stability and sustainable development of financial markets. Thus, this paper intends to analyze the financial regulation strategies through evolutionary game theory. In this paper, the delayed replication dynamic equation and the non-delayed replication dynamic equation are established, respectively, under different reward and punishment mechanisms, and their stability conditions and evolutionary stability strategies are investigated. The analysis finds that under the static mechanism, the internal equilibrium is unstable, and the delay does not affect the stability of the system, while in the dynamic mechanism, when the delay is less than a critical value, the two sides of the game have an evolutionary stable strategy, otherwise it is unstable, and Hopf bifurcation occurs at threshold. Finally, some numerical simulation examples are provided, and the numerical results show the correctness of the proposed algorithm. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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13 pages, 34699 KiB  
Article
From the DeGroot Model to the DeGroot-Non-Consensus Model: The Jump States and the Frozen Fragment States
by Xiaolan Qian, Wenchen Han and Junzhong Yang
Mathematics 2024, 12(2), 228; https://doi.org/10.3390/math12020228 - 10 Jan 2024
Viewed by 1047
Abstract
Non-consensus phenomena are widely observed in human society, but more attention is paid to consensus phenomena. One famous consensus model is the DeGroot model, and there are a series of outstanding works derived from it. By introducing the cognition bias, resulting in over-confidence [...] Read more.
Non-consensus phenomena are widely observed in human society, but more attention is paid to consensus phenomena. One famous consensus model is the DeGroot model, and there are a series of outstanding works derived from it. By introducing the cognition bias, resulting in over-confidence and under-confidence in the DeGroot model, we propose a non-consensus model, namely the DeGroot-Non-Consensus model. It bridges consensus phenomena and non-consensus phenomena. While different in meaning, the new opinion model can reproduce the DeGroot model’s behaviors and supply a series of interesting non-consensus states. We find frozen fragment states for the over-confident population and time-dependent states for strong interaction strength. In frozen fragment states, the population is polarized into opinion clusters formed by extremists. In time-dependent states, agents jump between two opinions that only differ in the sign, which provides a possible explanation for the swing in opinions in elections and the fluctuations in open questions in the absence of external information. All of these states are summarized in the phase diagrams of the self-confidence and the interaction strength plane. Moreover, the transition scenarios along different parameter paths are studied. Meanwhile, the influence of the nodes’ degree is illustrated in the phase diagrams and the relationship is given. The finite size effect is found in the not quite over-confident population. An interesting phenomenon for small population sizes is that neutral populations with large opinion variance are robust to the fluctuations induced by a finite population size. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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17 pages, 1116 KiB  
Article
Coupled Propagation Dynamics of Information and Infectious Disease on Two-Layer Complex Networks with Simplices
by Zhiyong Hong, Huiyu Zhou, Zhishuang Wang, Qian Yin and Jingang Liu
Mathematics 2023, 11(24), 4904; https://doi.org/10.3390/math11244904 - 8 Dec 2023
Cited by 3 | Viewed by 1365
Abstract
The mutual influence between information and infectious diseases during the spreading process is becoming increasingly prominent. To elucidate the impact of factors such as higher-order interactions, interpersonal distances, and asymptomatic carriers on the coupled propagation of information and infectious diseases, a novel coupled [...] Read more.
The mutual influence between information and infectious diseases during the spreading process is becoming increasingly prominent. To elucidate the impact of factors such as higher-order interactions, interpersonal distances, and asymptomatic carriers on the coupled propagation of information and infectious diseases, a novel coupled spreading model is constructed based on a two-layer complex network, where one layer is a higher-order network and another layer is a weighted network. The higher-order interactions in information propagation are characterized using a 2-simplex, and a sUARU (simplicial unaware-aware-removed-unaware) model is employed to articulate information propagation. The inter-individual social distances in disease propagation are represented by the weights of a weighted network, and an SEIS (susceptible-exposed-infected-susceptible) model is utilized to describe disease propagation. The dynamic equations of coupled spreading are formulated utilizing the microscopic Markov chain approach. An analytical expression for the epidemic threshold is obtained by deriving it from the steady-state form of the dynamic equations. Comprehensive simulations are conducted to scrutinize the dynamic characteristics of the coupled spreading model. The findings indicate that enhancing the effects of higher-order interactions in information propagation and increasing inter-individual social distances both lead to higher outbreak thresholds and greater spreading of diseases. Additionally, a stronger infectivity among asymptomatic carriers and an extended incubation period are favorable for the outbreak and spread of an epidemic. These findings can provide meaningful guidance for the prevention and control of real-world epidemics. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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19 pages, 7364 KiB  
Article
Aspiration-Based Learning in k-Hop Best-Shot Binary Networked Public Goods Games
by Ziyi Chen, Kaiyan Dai, Xing Jin, Liqin Hu and Yongheng Wang
Mathematics 2023, 11(14), 3037; https://doi.org/10.3390/math11143037 - 8 Jul 2023
Cited by 1 | Viewed by 1167
Abstract
In public goods games, it is common for agents to learn strategies from those who possess the highest utility. However, in reality, because of the lack of information, strategies and utilities from others cannot be obtained or predicted during learning and updating. To [...] Read more.
In public goods games, it is common for agents to learn strategies from those who possess the highest utility. However, in reality, because of the lack of information, strategies and utilities from others cannot be obtained or predicted during learning and updating. To address this issue, we introduce a learning update mechanism based on aspirations. To make this model more universal, we study goods that can be shared with k-hop neighbors. Additionally, when a free rider accesses an investor, it is required to pay an access cost to him. We investigate the influence of aspiration, shared scope k, and access cost on the social invest level and utility. It is shown that large shared scope k, moderate aspiration, and moderate access cost are conducive to the maximum utilization of social benefits. However, with low aspiration, the utilities of investors are very close and limited, while both the high aspiration and high access cost could disrupt the social stability. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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15 pages, 1595 KiB  
Article
Paid Access to Information Promotes the Emergence of Cooperation in the Spatial Prisoner’s Dilemma
by Haodong Niu, Keyu Li and Juan Wang
Mathematics 2023, 11(4), 894; https://doi.org/10.3390/math11040894 - 10 Feb 2023
Viewed by 1481
Abstract
In biological evolution, organisms that are more adapted to the environment tend to survive better, which can be explained in part by evolutionary game theory. In this paper, we propose an improved spatial prisoner’s dilemma game model, which allows the focal player to [...] Read more.
In biological evolution, organisms that are more adapted to the environment tend to survive better, which can be explained in part by evolutionary game theory. In this paper, we propose an improved spatial prisoner’s dilemma game model, which allows the focal player to access the strategy of other agents beyond their nearest neighbors with a specified probability. During the strategy update, a focal player usually picks up a randomly chosen neighbor according to a Fermi-like rule. However, in our model, unlike the traditional strategy imitation, a focal agent will decide to update their strategy through the modified rule with a specific probability q. In this case, the focal agent accesses n other individuals who have the same strategy as the imitated neighbor, where the information accessing cost needs to be paid, and then compares their discounted payoff with the average payoff of those n+1 agents to make the decision of strategy adoption; otherwise, they only refer to their own payoff and their neighbor’s payoff to decide whether the strategy spread happens. Numerical simulations indicate that a moderate value of n can foster the evolution of cooperation very well, and increase in q will also improve the dilemma of cooperators. In addition, there exists an optimal product of n×c to cause the emergence of cooperation under the specific simulation setup. Taken together, the current results are conducive to understanding the evolution of cooperation within a structured population. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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16 pages, 13486 KiB  
Article
The Sense of Cooperation on Interdependent Networks Inspired by Influence-Based Self-Organization
by Xiaopeng Li, Zhonglin Wang, Jiuqiang Liu and Guihai Yu
Mathematics 2023, 11(4), 804; https://doi.org/10.3390/math11040804 - 5 Feb 2023
Cited by 3 | Viewed by 1380
Abstract
Influence, as an inherently special attribute, is bound to profoundly affect a player’s behavior. Meanwhile, a growing body of studies suggests that interactions among networks may be more important than isolated ones. Thus, we try our best to research whether such a setup [...] Read more.
Influence, as an inherently special attribute, is bound to profoundly affect a player’s behavior. Meanwhile, a growing body of studies suggests that interactions among networks may be more important than isolated ones. Thus, we try our best to research whether such a setup can stimulate the sense of cooperation in spatial prisoner’s dilemma games through the co-evolution of strategy imitation and interdependence networks structures. To be specific, once a player’s influence exceeds the critical threshold τ, they will be permitted to build a connection with the corresponding partner on another network in a self-organized way, thus gaining additional payoff. However, a player’s influence changes dynamically with the spread of strategy, resulting in time-varying connections between networks. Our results show that influence-based self-organization can facilitate cooperation, even under quite poor conditions, where cooperation cannot flourish in a single network. Furthermore, there is an optimal threshold τ to optimize the evolution of cooperation. Through microcosmic statistical analysis, we are surprised to find that the spontaneous emergence of connections between interdependence networks, especially those between cooperators, plays a key role in alleviating social dilemmas. Finally, we uncover that if the corresponding links between interdependence networks are adjusted to random ones, the evolution of cooperation will be blocked, but it is still better than relying on simple spatial reciprocity on an isolated lattice. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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Review

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25 pages, 481 KiB  
Review
Data Assimilation for Agent-Based Models
by Amir Ghorbani, Vahid Ghorbani, Morteza Nazari-Heris and Somayeh Asadi
Mathematics 2023, 11(20), 4296; https://doi.org/10.3390/math11204296 - 15 Oct 2023
Viewed by 2146
Abstract
This article presents a comprehensive review of the existing literature on the topic of data assimilation for agent-based models, with a specific emphasis on pedestrians and passengers within the context of transportation systems. This work highlights a plethora of advanced techniques that may [...] Read more.
This article presents a comprehensive review of the existing literature on the topic of data assimilation for agent-based models, with a specific emphasis on pedestrians and passengers within the context of transportation systems. This work highlights a plethora of advanced techniques that may have not been previously employed for online pedestrian simulation, and may therefore offer significant value to readers in this domain. Notably, these methods often necessitate a sophisticated understanding of mathematical principles such as linear algebra, probability theory, singular value decomposition, optimization, machine learning, and compressed sensing. Despite this complexity, this article strives to provide a nuanced explanation of these mathematical underpinnings. It is important to acknowledge that the subject matter under study is still in its nascent stages, and as such, it is highly probable that new techniques will emerge in the coming years. One potential avenue for future exploration involves the integration of machine learning with Agent-based Data Assimilation (ABDA, i.e., data assimilation methods used for agent-based models) methods. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Evolutionary Game Theory)
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